I paid the same for that a year ago, so it hasn't really dropped in price which is annoying. Actually I think it's all down to Brexit, an i5 6600k is at least £20 more than when I got one...
UserBenchmark puts it a decent pace above. 55th ranking vs 122nd ranking. i5 is future proofing to an extent that your i3 isn't.
This is the thing with PC gaming, it is very easy due to the largely modular nature of things to get a good, Medium settings playing PC for a good price, but there's always the temptation to just go YUGE and future proof yourself. Rainbow 6 Siege lets me see how much of my VRAM is being drawn by its settings (which is a lovely touch) and it's currently on ultra 1080p drawing 2.6GB of a possible 8gb.
This is because I will be poor in 3 years time and I will be kissing myself for my stupid blitz spending.
You may consider it quite large, and I don't know if you're into white, but it's a decent price for a decent case. I think Tempy got an R4.
For the CPU, your choices should probably be (ascending in price): i3 6100/i5 6500/i5 6600k/i7 6700k. Choose whaterver fits your budget, if it's just for gaming don't bother with the 6700k.
I have the r4 I believe yes, be warned it is fucking huge and very heavy with all the bits in (bearing in mind I have a 1070 which is a fearsomely heavy bit of kit)
MY flat mate got a pre-built with insurance and all that, and watercooling. It cost him more than I paid (insurance, got made by people etc) but the case is so much smaller.
Minimal differences in gaming, the main difference with fewer cores is usually lower minimum FPS, which can mean more stuttering at times. They are both 4 thread CPUs, the i5 just has 4 physical cores while the i3 utilises hyperthreading on it's 2 cores.
I would go for the i3 6100 if you need to save some pennies. You can always upgrade and slap a shiny new Kabylake CPU in there in the future if you feel the need.