r3-1200 has a passmark rating of 6857 and a single thread rating of 1717.
By comparison, the A10-7860k has a rating of 5138 and a single thread rating of 1583.
It is the single thread performance that is most important for games.
So far, so good, ryzen is better.
I might suggest a $90 G4620, passmark 5319, single thread 2132.
A B250 lga1151 motherboard will be about $65, and 8gb of ram about $70.
The psu you need is determined by your graphics card.
Here is a chart:
http://www.realhardtechx.com/index_archivos/Page362.htm
Whatever you do, DO NOT buy a cheap psu.
Here is a chart:
http://www.tomshardware.com/forum/id-2547993/psu-tier-list.html
Tier 1 0r 2 is best. Seasonic is always good.