jerryc41 Loc: Catskill Mts of NY

Lots of choices, and you're smart to aim for under $500. Make it fun - not a chore.

Begin with the camera on Auto and concentrate of good composition.

Some useful sites -
https://digital-photography-school.com/11-tips-for-beginner-photographers/
https://expertphotography.com/a-beginners-guide-to-photography/
https://www.makeuseof.com/tag/5-photography-tips-for-beginners/

Compact cameras -
https://www.pcmag.com/article2/0,2817,2401971,00.asp
https://www.dpreview.com/reviews/2017-roundup-compact-enthusiast-zoom-cameras
https://www.techradar.com/news/best-compact-camera

Compact under $500 -
http://thewirecutter.com/reviews/best-point-and-shoot-under-500/
http://www.bestproducts.com/tech/gadgets/g706/point-and-shoot-digital-cameras/

Camera comparison sites -
Read comparisons and specs, and decide what features are important to you.
(Reviews) https://www.youtube.com/user/TheCameraStoreTV/videos
http://www.cameradecision.com/
http://cameras.reviewed.com/
http://camerasize.com/
http://www.imaging-resource.com/IMCOMP/COMPS01.HTM
http://snapsort.com/compare
http://www.dpreview.com/products/compare/cameras?utm_campaign=internal-link&utm_source=mainmenu&utm_medium=text&ref=mainmenu

Scruples Loc: Brooklyn, New York

Welcome to the Ugly Hedge Hog. It is great to be here and I'm sure you'll agree. Best thing to do is just get out and do photography. It doesn't have to be a wild exotic place like Myanmar. A local trip around the neoghborhood or on the other side of town. How about a botanic garden or zoo or aquarium.
As for cameras, many manufacturers make reasonably priced cameras that won't break the bank. While I'm a Canon guy, there is nothing wrong with Nikon.
Hang out at some gallery. See what other people photograph. Happy Shooting

RKL349 Loc: Connecticut

I might suggest a mirrorless interchangeable lens camera. They are available Factory reconditioned for extra savings. You can find cameras and lenses in great condition, preowned from KEH and MPB, at great savings, to mention a few of the more popular sales outlets. Whatever you do, look for a local night school or community college to learn the basics, which will make your learning experience and future photography more enjoyable.

art pear Loc: North Dakota

Get a used Nikon D7000.

dsmeltz Loc: Philadelphia

I am going to echo the comments you have received regarding mirrorless cameras. At this point you will probably be better served with one of the two mirrorless cameras you are already considering.

They are lighter and easier to deal with.

They both provide a great zoom range and will allow you to experiment.

You will not be locked into a system should you decide to upgrade at a later date.

Should you decide to upgrade to a more robust system down the road, advances in tech, price reductions and your improved knowledge from experience will position you to make a better choice.

And with either of the two, you will have a great second camera (there are two of you)

BuckeyeBilly Loc: St. Petersburg, FL

Welcome to UHH, Steve and your wife. I personally have the Canon SX530 and am very pleased with it. It is a refurbished camera which means that Canon's own technicians have reconditioned a camera to like-new condition and they give you a 1-year warranty to boot. Mine looks and performs great! Right now you can get one from Canon for $199.99. Get it
You'll love taking photos of the moon or that exotic bird perched in a tree 100 yards away. Go here:
https://shop.usa.canon.com/shop/en/catalog/powershot-sx530-hs-refurbished

sloscheider Loc: Minnesota

AND currently $300 off so $500 right now

WarpedWeaver

I got back into photography a couple of years ago with a Nikon Coolpix P610 and I still use this as a "grab and go" camera. I am going to "jump ship" with Nikon, however, and am looking seriously at a Fujifilm XT3 now that I have outgrown the Coolpix. Going with the Powershot or Coolpix will give you the opportunity to play with the exposure triangle and learn before committing a lot of money on something you may learn is not your "forever" hobby. I hope you and your spouse enjoy it as much as the rest of us here!

gvarner Loc: Central Oregon Coast

Start cheap and simple. Try to find two cameras for $500, preferably pocketable. Upgrade later and sell them or keep them for backups. If you’re not computer savvy, you better bone up or you’ll get frustrated pretty fast. Digital cameras are just another computer accessory. You don’t have to learn all of a camera's functions, modes, and scene choices but you should explore them to see if any work for you. Viewing photos on a monitor or TV or printing photos is a whole different realm to explore so be prepared for the challenges. Start as simple as possible and study and practice. Digital film is cheap. Good luck.

billnikon Loc: Pennsylvania/Ohio/Florida/Maui/Oregon/Vermont

OK, I am over your budget by $200.00 but I believe it is a good investment for you. Information below. This camera will allow you to grow into photography. Nikon d7200 new USA version, from B&H
https://www.bhphotovideo.com/c/product/1127271-REG/nikon_1554_d7200_dslr_camera_body.html?sts=pi-ps

Plus a Nikon 35 mm 1.8 lens.
https://www.bhphotovideo.com/c/product/731085-REG/Nikon_2183B_Refurbished_AF_S_Nikkor_35mm.html?sts=pi
Again, I am having you go over your budget. But the D7200 is a proven winner. I am sure you will enjoy the camera and again the body will allow you to grow in photography.

Earnest Botello Loc: Hockley, Texas

Welcome to the Hog Steve, enjoy.

RSpinney Loc: Maine

Good morning, Steve. I have a Kodak Pixpro AZ901 and I love it. It has everything from Auto to Manual to Special Settings. I've zoomed to take a photo of a Great Blue Heron across a pond and then, feeling a tickle on my left hand, was quickly able to take a closeup of a dragonfly resting on my index finger. It is a Bridge Camera. No changing lenses of a DSLR. Look for the camera here: https://kodakpixpro.com/cameras/astro-zoom/az901. Note the "Smart Ring" that can be programmed to change a selected setting quickly. No matter the camera you purchase, don't get suckered into buying accessories with the camera purchase. I did from someplace in Long Island, NY. I got a cheap and crummy tripod that was worthless among other things. (This was NOT with the currently described camera which I purchased directly from the link above.)

dbfalconer Loc: Salida CO

Definitely look closely at Sony a6000 mirrorless. An excellent camera and much lighter then most other dslrs. Be sure to actually handle a few cameras before you decide. I began this hobby a short time ago too, when I retired. I love it.
Look for a local photography club—especially a low-key one that focuses on learning and fun rather than competition. A great source for information and support and camaraderie. Good luck!

olemikey Loc: 6 mile creek, Spacecoast Florida

Welcome to the Hog!! High quality and Advanced Point & Shoot cameras are certainly a great way to find out if you picked the right hobby (together or separate). The better models do a fine job and are reliable, and the two you mentioned would be good starters, and could serve you well for a long time. I have a little Canon A590 I bought years ago (08) that still works like a champ, and have owned Nikon L830, L840 and P530 models bought for their ever increasing zoom range and other capabilities (my son has the L830/840 duo now, and says he uses them a lot). I traded the P530 in to help cover a used Nikon D7100, got nearly what I paid for it.

Once you develop your technique you can make photos anyone would be proud of and be proud to share. The only problem with superzoom cameras is when you move up to cameras with other lens options, you will miss that big zoom! The newer P&S cameras allow for shooting in Manual, as well as many auto/scene modes, so you can learn with them, or just continue to enjoy the automation and internal computer power.

You are going to get a lot of "go full DSLR or Mirrorless" but that is not as important at this step, finding out if the two of you are going to enjoy the hobby together is probably more important, as you can make other adjustments once you know the answer to that. Two cameras that are alike or very close might be helpful too, that way one answer fits both, so to speak, when it comes to challenging adjustments and learning curve (AndyH speaks well to that, and check out his thread on the 2 systems, <$2K challenge).

If you don't mind buying used, you can pick up excellent equipment at a greatly reduced price (with a warranty) from several high quality re-sellers that are often mentioned on the forum. I've been shooting seriously since 1970, last new camera I bought was a Pentax ME Super in the 80's (and I have a room full of cameras and lenses/gear), during all that time only two cameras bought used have failed, but I bought them so cheap that it didn't matter (they look great sitting in the case with a nice old lens attached). For used, local camera shop, MPB.com, KEH, Usedphotopro(Roberts) Hunt's, B&H, Adorama, Cameta and others.... for new Hunt's, B&H, Adorama, Cameta, Best Buy, Robert's, Local Camera Shop and others. Many camera company website (Nikon, Canon and the rest) also offer what are called "Refurbs" that are cheaper, have a warranty, fully checked out and will work just fine.

I'm getting long winded here, but you came to a good place; You will get lots of good advice and help here, anything else (opinions and rants on all sorts of things), just ignore it.

Architect1776 Loc: In my mind

Of those options which are all excellent the Rebel T6 is by far the best.
Larger sensor gives generally better photos. If you decide that you really like photography there are millions of used EF and EF-S lenses very inexpensive and ALL will fit and work 100% on that Rebel. NO other system has such 100% compatibility.
The Rebel cameras will be a great upgrade from the other 2 choices, are lightweight and give incredible photos.