Considering your level of experience, you might also want to look at Adobe Elements (currently version "2018", though they usually release a new version each Fall).

Elements is comprehensive and includes aspects of both Lightroom and Photoshop. It also has built in support.... a "guided" Beginner mode, less guided Intermediate mode and an unguided Expert mode. You choose which you want to use and can switch between them at any time. Elements is designed to be a stand alone program that's fairly easy to use and able to meet most peoples' actual image editing needs.

LR and PS actually are two different programs, designed to work together and complement each other. LR is primarily an organizing and archiving program, with light image editing and batch RAW conversion capabilities. It's not really designed to "finish" images to a high degree. PS is the "Mack Daddy" of all image editing and optimizing programs, highly complex and full featured for those purposes, but with minimal organizing and archiving capabilities. LR is designed to rapidly work through a large volume of images, spending only a few seconds to a couple minutes on each, sorting and selecting among them, adding keywords, building and maintaining your library of images, batch uploading proofs/thumbnails to online galleries, making catalogs or slide shows, etc. Photoshop is more "one image at a time", possibly spending hours working on it to fully finish it for high usage such as printing.

LR is fairly complex, but not bad and probably no more difficult to learn than Elements (though Elements contains more automation). With either of them, one or two books and a month or so working with them and you'll likely feel comfortable.

Photoshop is far more complex... I seriously doubt anyone actually uses all its features and capabilities. I've been working with it since version 4 in the mid-1990s and would guess I don't use more than about 20 or 25% of what it can do. With PS you should plan to buy a small stack of books, take a years worth of college level classes and probably spend most of a year óf regularly working with it to get truly comfortable.

Neither LR nor PS have any "built in support". You have to look elsewhere for guidance learning to use them. They also don't contain a whole lot of automation.

There is extensive outside support for all three... books, classes, online tutorials (best, IMO, to learn specific techniques... not for general learning and familiarization). There are also a variety of plug-ins for all three. Most for Photoshop, but also quite a few for LR and Elements.

Elements is sold outright... perpetually licensed... for about $90 (sometimes goes on sale for less). There are limited updates and usually a new version each year (which you don't need to update to unless you get a new camera that's not supported by an older version of Elements or unless the new one has some new features added that you want).

PS and LR are now only available via subscription.... $120 a year. You get them both for that (not available individually). If you let the subscription lapse, they stop working (but your images remain... though you may have trouble finding specific ones without your LR catalog).

Elements is referred to as an "8-bit" program. This means that it can only save 8-bit types of image files, once you are done post-processing them. LR and PS can provide 16-bit files.

Actually, at the core of all three is Adobe Camera Raw (ACR), used to convert camera RAW files into a usable format (assuming you set your camera to save RAW, in addition to or instead of JPEGs). This is fully integrated into both Elements and Lightroom. In order to update ACR in either of them, you have to update the entire program. Photoshop has a sub-module containing ACR... that can be updated separately.

When you work on a RAW file, all three treat it similarly. While there are a few functions that are not usable in Elements until an image has been converted to an 8-bit file, it's mostly just when you go to save the image that Elements limits you to 8-bit files such as JPEG or GIF or PNG and similar. Frankly, this is all most photographers ever actually need. JPEGs are required by a lot of printers and are the standard for online display, slide shows, email attachments and much more.

16-bit files which both LR and PS can produce (such as TIFF or PSD and similar) may be needed for commercial work. If wanting to close a file and re-open it for additional work later, it can be advantageous to save it in one or the other of the 16-bit formats. Sometimes a client specifies one of these formats so that additional work can be done on the image later, to suit their purposes.

You can download a 30-day trial of any of these direct from the Adobe website. That would be good with Elements, to see how you like it. 30-days might also be adequate to try out Lightroom. But in either case, for anyone who has never used them, I'd recommend buying in advance and at least scanning through one or more of the guide books for the specific program, and then keeping the book(s) handy to make best use of the trial period. I would not recommend trying to evaluate both at the same time. And a 30-day trial of Photoshop is probably not sufficient time for anyone other than experienced users. A new user would only be getting started and not really up to speed using it, in just 30 days.

Photoshop in its perpetually licensed version used to cost upwards of $600 for the initial full installation, then major version upgrades costing around $200 to $250 were rolled out every few years. Several years ago Adobe switched to the subscription only model with PS.... tried asking more at first, but finally ended up bundling it with LR for $10 a month (when you prepay for a year).

Lightroom hasn't been around as long, but went through 6 major versions, each selling for around $150, before it too was converted to only selling by subscription last year (and only bundled with PS). You'll hear various things about this from users... good and bad... about havign to subscribe. Using PS for nearly 25 years and LR since it was introduced, but only upgrading PS every other version... because it was being rapidly developed, LR more frequently (I think I only skipped one version)... my cost probably worked out about the same as what the subscription now costs. I budgeted roughly $350 every three years for PS and LR, before it went subscription-only.

At one time PS was pretty much "pro only", due to its initial cost. At 1/4 the price, Lightroom probably saw much wider sales, but was used by a lot of people as a stand-alone (which is possible, though pretty limiting). Now that the subscription sounds like a bargain (it's really no different for me), there are lots and lots of far less experienced buyers. There's been a huge increase in "help me with PS/LR" posts on photography forums the last few years. I can't help but wonder how many try PS... in particular... only to find it overwhelming and eventually give up or only use it in a very limited way. Adobe doesn't care... they've made a fortune with the subscription sales model and vastly expanded number of buyers... uh, subscribers, I guess! (Not "users"... because, who knows if they really do use it.)

Hope this helps you make a decision.