Should I go with a Ryzen 5 1400, or a i3-8100?
We need a little more info than that. What GPU/monitor you'll be using, what games you'll be playing and at what settings, etc.
GPU I will be using a 1060 3gb. Just a 24" 1080p 60hz monitor. I will be playing games like PUBG, Overwatch, CSGO, and Rainbow Six Siege.
A Ryzen 3 1200 with a $70-ish B350 boad will be plenty
Best guide for parts choices is always researching in use Benchmarks for your intended uses.
Most places will use synthetics since they are easily replicatable but they have little bearing on real world uses.
That all depends on what you are doing.
Only gaming purposes. Titles like PUBG, Overwatch, CSGO and Rainbow Six Siege.
Go with the 8100. Much better single-core performance will show through much better in games.
1500X on A320 would be about the same implementation price and offer the best performance of the bunch IMO.
I3 8100 is better for gaming. If you can try to get an i5 8400 as it has significantly better performance.