you can target just about any hardware with godot. Just tweak your quality settings and don't use large PBR Materials. If you are doing 2D it will definitely run and if you are doing 3d then as long as it can run GLES 2 or 3 you will be fine. Obviously the more powerful the pc the more rendering features you can enable but for a toon solid color game with optimized meshes (either just built in primitive shapes or low poly imports) the only thing stopping you from getting started creating right now is your imagination or motivation :) Best of luck! Have fun creating! The engine editor is a very tiny download on the main site and that is all you need to get going.
Take a look at the docs, as well as the built in editor docs, and youtube tutorials if that is your style.
If you get better hardware later you can up the quality of the render settings and your materials a lot easier than other engines too so there is really no reason not to start simple. From what I just looked up it seems your card can handle AAA games at 30 fps so theoretically you can have some more demanding render features on your hardware if you optimize it and expect low frames.
On a side note:
One thing you really need to keep in mind just starting out with programming, creating something, or learning anything new in general, is start small. I have done what you are trying to do many times and it was a great learning experience but I never ended up with an end result. If you try and create a Massive Multiplayer, Fps, , Story Mode, and high quality graphics (models / animations / textures) you need to remember that the games like this are usually made in large teams at studios with hundreds of people. Each section is a large task on itself. Learning the engine will make development take a little longer at first. FPS has lots of things you need to add game mechanics wise. Networking is its whole own beast and networking + fps means it has to be extremely responsive networking and also secure / server sided to avoid cheating which is no easy task to get working. Story mode means hours of script writing, character development, quest systems, voice acting if you want voices, items, large maps, and many many many assets which directly relates to open world and graphics. Open world unless you do it procedural style like minecraft takes a tremendously long time to make a map for even for large teams of artists and the larger your open world is and the more quests you have the more assets (models, buildings, shaders, textures for all of these, etc) you need basically exponentially increases. Lastly, these assets, esspecially in quantities needed for this scale, take a long time and lots of 3d art skill to make.
ps. Godot networking is fairly rudimentary and not designed for 100+ player games or massive word synchronization so you would likely need to write your own networking library or port one into a godot module or into the base engine code itself in c++
TLDR; If you don't have a team of your friends also working on this, (one for story, one for assets, one for network engineering, a few game code) then I would highly recommend lowering the scale of your project and make a stylized indie game that can be finished soon and be a completed success rather than a WIP "Masterpeice AAA Monster Scale Megagame" that will be abandoned later down the road when you inevitably loose interest in the project due to lack of result. <- I have many of these.
This is all just my opinion of course but I say this because I have done this many times and have so so so so so many unfinished projects because my scope was way to big. I've heard many people say this same advice, make something you can make, not something you want to be able to make. Did I learn a lot from the projects I never completes? Of course! I learned tons about all the frustrating things I ran into like how to get networking to work for example. But at the end of the day it is nice to have an end result that you can get feedback on and then move onto your next project already knowing how to use the engine, knowing what mistakes to avoid, some tricks to do certain things, etc. At the end of the day your 10th simple game is always going to be better than your first ever massive game, and you'll have a lot more fun making the smaller projects starting out too.