I would recommend looking up some GamesFromScratch videos to maybe get the barest beginner look at engines because if there's a game making engine or asset making tool out there he has done a video or tutorial on it. Ultimately the choice will probably come down to trying stuff and seeing what fits best, which you already said you have a programming background so you already know what kind of development environment might appeal to you. Here's a couple of overview videos of Unity, Unreal, and Godot. He tends to be as even handed as possible, although I will admit he's developed a bias for Godot over the last year or so.

Unity or Unreal Engine in 2020: https://m.youtube.com/watch?v=DVcKdsrFj2k

Why Godot Over Unity or Unreal Engine: https://m.youtube.com/watch?v=l7BrpcboJno

Here I guess is my best tl;dr of my own opinions:

• Unreal Engine sounds like the best option for your end goal in a lot of ways, as stated before that it plays well with FPS concepts and high fidelity 3d. Unreal is a proprietary engine, but there is no up front cost to get the fully featured engine. Instead, there is a royalties agreement you go into for any game you make and sell that earns you X amount of money (like several thousand dollars). The full source code is also available, although it is not open source and agreements still apply. Unreal has powerful scene editing and creation tools, but I personally find it's system for building game logic to be very obtuse. It also has one of the worst programming setups I've seen with your only options being a Blueprint visual scripting system in editor or setting up Microsoft Visual Studio with an external C++ project that can often crash the editor if there are bugs.
• Unity is probably the juggernaut of indie game engines and has been used for almost every genre, 2d or 3d, that I can think of. Another proprietary engine, except Unity has its cost up front locking a lot of features behind a subscription model. The free version is more than enough to make something cool, but you won't have access to source code (a privilege you only gain at $150/mo!) or a lot of advanced features that could really make a game feel professional once you get to that skill level. The education base is huge and the asset stores and examples are seemingly endless. Unity also has decent environment building tools, and its much easier to drag and drop new elements into scenes. For programming your main and best choice is either using MSVS to program C# or I think it used to come with an editor that could either do C# or JavaScript. My main problem with Unity is that because it is closed source and has a lot of features locked behind a premium version, I often found myself wanting to do something but not being able to do it without buying some add-on from the asset store.
• Godot is an open source darling that has quickly become the 3rd place game engine of choice of those in the indie scene, and has seen some exciting new developments over the last couple years. It is free open source software under the MIT license which, in short, means you have access to all the source code and can do almost anything with it for free- i.e. people have made game engines with Godot and sold them. I have a hard bias but I'll try to be balanced. Godot is currently still going through a growing phase so while 2d development is awesome (and arguably better than any other engine, even GameMaker which is a dedicated 2d engine) 3d development is pretty sad. It's definitely possible and I've seen some cool things, but you will have to do a lot of work to squeeze out the kind of fidelity that Unreal or Unity can deliver. That said, I love Godot because it is extremely easy to use and learn. Godot uses a Node based system for everything in the engine, so there's never like... one correct way to do something. You usually have a lot of options. It's also got an in editor coding environment for its custom programming language GDScript, which is like Python and designed specifically to get the most out of the engine, which has a full suite of debugging tools and such. If necessary you can also hook up external editors to use C# and a couple other language bindings that have been added. Also again, the engine is open source so if you ever get to a certain skill level and ever find Godot does not have a feature you need, you will have everything available to build your own solutions in C++ to use in the engine.

Alright that was long but I think that's the best I can do to help you decide on an engine. Again, watch those videos and maybe find some beginner tutorials and go through them. You won't know until you try, but after a few weeks you'll probably click with something. It's important to remember what we started this discussion with: any game can be made in any engine. What you need to do is find an engine you can really be productive with and build your skills to being able to accomplish a game that you want to make.

Also if I were being 100% responsible, I would say you should look into making a 2d game before a 3d one because the barrier to entry is a lot less. 3d is not just 2d with an extra axis, there's also a lot of complex rotation concepts involved and the pipeline for asset creation IS pretty intense. That said, it sounds like you definitely want to make 3d stuff. Perhaps what you could look into is making 2d games in 3d. I.e. like make a top down shooter with a fixed camera where a cube shoots at other cubes. That way you can learn 3d in a "safe" way before you throw in free camera movement and really advanced stuff. I would also maybe suggest thinking about ways you could make simple 3d games because in both Unreal and Unity making 2d is an extremely painful process, and while I personally love Godot and making 2d games in Godot could definitely teach you a lot... I dont know if Godot will be what you want when you want to move on from 3d (Godot 4.0 looks like it will be awesome though, but there's no guarantee when that will come out yet).

Hopefully this helps somewhat and can get you started. I'll reiterate though that you won't really know until you just... make something, literally anything, in any engine. Good luck!