I know when you say stroking out you get a new head or shorter piston rod. I have been looking and i cant find anywhere to order forged pistons. the static displacement im lost for that does it matter what number is for that or would i just say i want a lower one and tell them my goal hp

 

You generally don't have to replace the cylinder head when you stroke an engine. You just replace the crankshaft with one that has a little longer stroke, and then use shorter connecting rods so that the longer stroke doesn't push the pistons out the top of the block at the maximum stroke. For instance, the stock MINI bore is 77 mm and the stroke is 85.8 mm. If you lengthen the crankshaft stroke by 16 mm and shorten the connecting rods by 16 mm, you'll go from 1.6L to about 1.9L. Of course, now you're talking about a custom crankshaft, connecting rods and pistons.

As for static compression ratio, it's a measure of how much the air/fuel mixture gets compressed as the piston moves from the bottom of its stroke to the top. Higher compression ratios are good for more power, but a high compression ratio limits the amount of extra air/fuel you can shove into the cylinder without running into knocking/detonation problems. And since you're looking at high boost levels to get 300 HP, you're either going to have to lower the compression ratio or run a steady diet of ungodly-high octane racing fuel. Most small-displacement engines that are making that much power with turbochargers are either using very high redlines (like 8000+ RPM), or using lots of boost and a low static compression ratio, like 7:1 or 7.5:1.

At the power levels you're aiming for, you're kind of going beyond what's been done with the R56 (as far as I know), so you'll be better off consulting with a professional engine builder to see what it's going to take.