GSR>ALL

If you want to boost it, GSR is the best candidate because of its compression and price.
If you want to run all motor, GSR is the best candidate because of PRICE.

You can buy the GSR, swap it into your integra an it will be PLUG AND PLAY. H22 will not. And its not a great motor to boost either.

B20=Weak, barely stronger than an LS, thin sleeves make it hard to turbo.
ITR- $$$$$$$$ and not good to boost , compression is too high, pistons weak
H22- Not easy to swap, lots of wiring, horrible transmission, requires mount kits, alternator relocation sometimes, etc etc etc.

Do the GSR you will be much happier