You mention having and wanting to use some older lenses.... Be sure to consult the Nikon camera and lens compatibility charts and info available online.
https://www.nikonusa.com/Images/Learn-Explore/Photography-Techniques/2011/Which-Nikkor-is-Right-for-You/Media/NIKKOR-lens-compatibility-chart.pdfhttps://www.nikonians.org/reviews/nikon-slr-camera-and-lens-compatibilityhttp://www.kenrockwell.com/nikon/compatibility-lens.htm#afpThe D3000-series and D5000-series cameras you're considering, in particular, have some limitations. There are also some newer lenses that won't work fully on some D7000-series, etc. (though it may be "fixable" with a firmware update).
I've also heard that the D3400 is a downgrade from the D3300 in some ways. Might be worth tracking down one of the earlier models.
You can compare model features pretty easily at the B&H Photo website (up to four different models).
Another website that can be useful for comparisons is
http://cameradecision.com/compare/Nikon-D3300-vs-Nikon-D3400However, sometimes those sites overlook fine details such as the differences others have noted, where the D3300's built in flash is more powerful and the D3400 lacks a self-cleaning sensor, which the D3300 includes.
I've also noticed that the D3000-series models are hard to find sold as "body only". Most places only offer them with a kit lens or two, which you may or may not want (and often the second lens is the AF-P 70-300mm DX, which lacks VR.... which makes no sense since image stabilization is much more useful on telephotos such as that). "Body only" D5000-series model might be little or no more expensive than a D3000-series model with a kit lens.
D5000 series cameras have a number of upgrades, but I think the most important are their more advanced autofocus systems (more AF points to choose among, and more of those points are higher performance "cross" or "dual axis" type). The D5000 series cameras also typically have articulated LCD screens, which can be quite handy. Some of the other added features of the D5000-series may or may not be important to you (or me).... such as GPS, wireless connectivity, yada, yada.
D7000-series have a true pentaprism, where the D3000/5000-series use a pentamirror. The pentaprism generally makes for a bigger, brighter viewfinder, but adds cost and a bit of weight. D7000-series also have further autofocus upgrades, more weather sealing, usually higher continuous shooting frame rates, and are compatible with more types of Nikkors. They have an in-body focus motor to be able to autofocus some of the earlier AF Nikkors, which is something all D3000/5000 models lack.
D3000/5000 have top shutter speed of 1/4000 and 1/200 flash sync, and their shutters are probably rated for about 100,000 cycles. D7000-series have top shutter speed of 1/8000 and 1/250 flash sync, and a shutter rated for 150,000 cycles. D7000-series also offer micro focus adjustment feature to be able to fine tune the accuracy of AF lenses, which the "lesser" models lack. But D7000-series also are "beefier".... typically weigh in up to as much as a half lb. more than D3000/5000 series models.
Nearly all recent D3000, D5000 and D7000 series models use a similar APS-C size, 24MP sensor. HOWEVER.... D3000-series models are 12-bit, offering less color depth and less dynamic range than the 14-bit sensors found in D5000/7000. The latest D7200 and D7500 also have higher settable and usable ISO... there have been significant improvements made in that respect with the last one or two generation sensors.
Also do careful comparison if considering older used, refurbished or even recently discontinued models still available new. For example, one issue someusers had with D7100 was it's small image buffer.... It had to slow or pause to clear after only a short burst of images at high continuous shooting rates (which might be a problem to sports photographers, but not to landscape photographers). The D7200 saw a significant improvement in this respect.
And, the D7500 is actually slightly lower resolution at 21MP (vs 24MP in D7100, D7200 and recent D3000/5000 models). This is to allow it to shoot at higher frame rates than the other models.... 8 frames per second (vs 5 or 6 fps). The less crowded 21MP sensor also may make even higher ISO usable (and Nikon has made possible to set it ridiculously high, though users will have to decide whether or not the image quality at super high ISO is acceptable).
Touchscreen LCD monitors are found on some of the newer cameras.... which some people really like.
Another feature found on some recent models (D7200 and later?) is Anti-Flicker, which goes a long way to solving the age-old problem when shooting under fluorescent and similar lighting that cycles at 60hz (in the U.S.) and causes a lot of exposure/color tint problems for photographers. This feature found on recent Nikon and Canon (don't know about others) "senses" the peak output of the lighting and times the shutter release to coincide with it.... And it works! Where I used to see around half my images ruined when shooting under that type of lighting (and had to shoot lots and lots of extra shots to be sure).... Now using Canon with the Anti-Flicker feature I see very few images lost to exposure problems. I've heard the feature works just as well in Nikon cameras that have it.
So, a lot depends upon what, where and how you want to shoot.... You'll need to do careful study and comparison of models, taking your own requirements into consideration.
Besides used (which will typically be older models that were traded in), you also might want to look at refurbished and "open box". These are often demo units that have seen very little actual use, may have the same warranty as new, and often are the most recent and current models... at a bit of a discount. Just this year Nikon USA has begun selling refurbished directly via their website (the way Canon USA has done for several years). Might be worth a look. There are still some refurb Nikon found at the major retailers, too, as well as open box deals. So, shop around!
Hope this helps!