You can keep using your existing case. That Logisys case looks decent.
Everyone has a different belief in how to apply the thermal compound, but two major methods are -
1. Spread it thinly and evenly across the entire surface area of the core
2. Only drop in grain-sized drop in the center, and wiggle your heatsink on top of it a bit to spread it a little, then just install
I personally go with no.1 method, but no.2 works too.
But one thing is for sure: you do NOT want generous amount. No. You don't want thick amount of thermal compound applied, because then it'll make it heat up WORSE.
You also do not want to apply none, as these thermal compounds are designed to transfer heat off the core better.
As for the i5-2500k vs. i5-3570k, i5-3570k does have much better OC headroom than i5-2500k. It's just that i5-3570k needs a far better cooling than the i5-2500k to achieve the same overclock beyond 4.5 GHz. Basically, that Hyper 212+/EVO won't be enough, you need to be investing in something like Noctua NH-D14, Corsair Hydro H80+, etc. to control the heat for i5-3570k beyond 4.5 GHz where additional voltage will be needed.
Then again, you will be stuck at most, 4.8 or 4.9 GHz on i5-2500k. Few lucky samples hit 5.0 GHz. Ivy Bridge will probably hit 5.0 better if you have the cooling to support all the heat.
Yes, the ATX. I will make that note now. Same with US dollars.
HAF 912 Advanced (Plus) is better than the Storm Enforcer due to more fans included.
By the way, plain HAF 912 and HAF 912 Advanced / Plus is a two different cases.