No worries. We all build out first computer once.
YES. The PSU matters a lot. It's a 'forever' part that can live on in future builds. It's like a car engine.
Gaming is the equivalent of motor-racing. You need reliable, robust, and high-performance parts. When you are gaming there are huge, frequent, and short changes in voltage demands, and these have to be met by the capacitors in the PSUs. High-performance PSUs have high-performance capacitors that can take the thrashing and beg for more.. High-performance PSUs also deliver smooth power at the voltages they say they will. Other PSUs cry for mother and eventually fail (or not so eventually, like tomorrow fail)
For the budget you have you need a very good PSU.
The same applies to a good air cooler that would be a lot cheaper.
It's not exactly a beast. I have one, donated by a thankful parent. It certainly is good, but good for what? It depends on your needs.
Both NVidia and AMD have new GPU releases close enough to the horizon that I would be very conservative about my recommendations. At the moment, the price/performance for the GTX 980 is poor. for the price, it if better to go up to the GTX 980ti, and for the pesrormance it is better to overclock a GTX970.
If you want to do 1080p., the 970 is fine
If you want to do 2K, I'd suggest AMD or a GTX 980ti
If you want to do 4K, wait. here is not really good single GPU solution today.
Do not get a AMD 83xx if you plan to upgrade soon. You are wasting your money
AMD gives great price/performance, but not at this level, at the moment, with any product..