Raising compression with head gasket

As some of you may know from previous posts I've made, I'm getting ready to do some head work on my H23a. I was wondering how effective a thinner head gasket is in raising compression and increasing power safely, while still maintaining reliability. I really haven't heard any negative effects or necessary additional upgrades when upgrading the head gasket, except maybe premium gas, which I already use. I'll admit I am a beginner on this subject so any help is appreciated, thanks.