Wouldn’t let me select a case, but you can get a good one for $80-100 that comes with RGB fans. This should keep you under budget, and building a PC can be fun even if you’ve never done it before. Plenty of tutorials on youtube. The hardest part is finding a GPU. If this PC is primarily for flight simulators, INTEL is the way to go. the 11 series is currently the best CPU out for MSFS.
If you’re planning on overclocking the CPU or RAM, go for a better Motherboard - Specifically the ASUS ROG type. It’s the #1 overlooked item when PC building. You want a good MOBO to help with stable Overclocking. If not, this one will do.