Love building gaming computers and tinkering with different mixes of hardware. Check out my link below for my personal list of the best gaming PCs (helpful if you are also in a budget).
Message me if you need guidance on gaming hardware, I am always happy to help!
My advice as a newbie would be to just play around in PCPartspicker. See what you like, and research the individual items.
If not that, then just check out the builds on here already posted by other users. They are solid and they fit your budget
Yeah, I make a good habit of never having my batter in if I am just going to stay in one place. I do keep it charged when I take it out, but that's only because I plug it back in because I need portability.
Yup, check your temperatures. Often times if it is heating up too much, there can be some burnout in the card. If that is the case, update here with more information and we will help you.