Intel processors are faster than AMD processors. Even when you compare prices. Only in the bugdet-segment (aka low-performance) AMD can compete. For any gamer, an Intel CPU is strongly recommended.
Intel CPUs are relatively cool. Therefor there's no need to spend money on a custom cooler or fan.
The GPU is by far the most important part of any gamer's CPUs. Any money you can save from not buying over-expensive parts, you can, and you should invest in your graphics card. The GPU determines for 95% what framerates you will get. (CPU is a lot less important, but if you buy a CPU that is too slow, it might impact all games. Motherboards have zero impact on framerates. More RAM doesn't help a bit. HDD or SDD only help loadtimes).
16GB is still overkill. 4GB is not enough for a few games. 8GB is still the sweet spot. It won't be until a few years when 16GB will be the sweet spot. Buy 8GB now (2x4GB). You can always add 2x4GB later. Invest the $50 you saved in a faster videocard.
SSDs are very nice. I recommend them to all my friends and family that want to buy a new general-purpose machine. However, if you are a gamer, and you have a limited budget, then all extra money should go into your videocard. I'm not saying you shouldn't buy a SSD. But if it makes the difference between a good videocard and an even better one you can't afford otherwise, I'd go without the SSD. Just buy an HDD and put everything on it. You can always (6 months, 12 months, 24 months, whenever) buy a SSD and put it in yourself. Only drawback is that you probably will need to reinstall Windows (and all your games and applications). If you buy a SSD at the start, and a cheaper videocard, then if you later want to replace your videocard, all the money you invested in your first videocard will be lost.
If you are limited in budget, focus on 1080p gaming. 1080p is still a very nice resolution for gaming. Only a
few percent of gamers play at higher than 1080p. Higher resolutions are nice for people who do photo-editing and other static stuff. But for gamers the improvement is minimal. And higher resolutions will bring down your framerates (by significant factors, like it will half your framerates or worse). I wouldn't use a 1440p monitor for gaming if I got one for free.