For gaming, the difference a sound card would make compared to the inbuil on the motherboard will likely be unnoticeable.
You can get the Pentium G4560 for ~$40 less and you only lose a slither of performance.
You don't need an aftermarket cooler for an i3 6100 or G4560. The stock is sufficient. If you'd like to improve noise or aesthetics, go with the cryorig m9i. The 212 is not a good buy at that price.
The ram for 16gb is hugely overpriced. I won't need 16gb of ram for gaming ATM (8gb is sufficient), especially for a build of this budget.
Try fit in an SSD. Even 120gb is fine, (as mention) can store the OS and 1 - 2 game or possibly more depending on their sizes. The SSD makes the computer feel a lot more responsive, especially when recently turned on.
With the saved money you can probably affor an RX 470/570, having much better performance at 1080p and can play most games at high+ settings with 60fps
The power supply is mediocre quality and putting the money into a better PSU is well worth it. You can currently get the m12ii 520w for roughly the same price which is a good PSU. If that's not available I'd recommend the corsair cx450m
I recommend looking at Ethernet/ power line adaptor possibilities before WiFi.