Well I'm nowhere near you, but personally, I'd go with the h22 build, and save up to boost the h22 later on. Asfar as time goes, I think that the h22 would take a bit more time to do. The shop that I go to would do the swap for me in 5 business days, but shops usually take longer than what they quote you.
Asfar as cost goes, if you're looking to get a good or great turbo build, it'll cost more than the h22 swap, especially if you're piecing it all together yourself and getting high end parts.
Gt35r T3 1300
FMIC 400
Blitz BOV 275
Tial Wastegate 250
Catchcan 150
Oil Cooler 100
Exhaust Manifold 150
Downpipe 170
DSM 1000cc Injectors 300
Walbro Fuel Pump 110
Total: 3205
That's everything I've sourced together for just the turbo setup, and I'm still missing some things. You'll still have to figure the price for new pistons, rods, bearings, sleeving, etc in order for the f23 to handle high psi's. I don't know if the f23 can handle the boost setup that I was sourcing, because that setup was meant for an f20 that I want.
Another thing you'd probably consider with boosting your f23 would be to swap out the tranny for a 5/6spd. So IMO, H22 it first, then decide where you want to go from there ..