The main risk of overclocking is always temperature. However, as long as you have a good cooler, which is pretty much any cooler that costs over £20, you are good to go.
Basically as long as you keep a watch on your temperatures and make sure that CPU temperature doesn't hop over 55-60C you should have nothing to worry about.
Also overclocking is not something you should be too concerned about at the moment as even without overclocking both i5-6600K and i5-7600 can handle any current game with no struggles.

About the input power, power supplies aren't that expensive so getting something like 400W instead of 350W shouldn't make a big difference in your budget.

Overall from what I can see i5-7600 would only be superior in case you get no graphics card as it has better onboard graphics so even paying those few extra pounds for better PSU should pay off