my bro has a b16 head on a B20z2, which has a higher compression ratio than the b20b4. I've looked over several dyno charts of b20/vtec setups with both b16 and b18 heads. the b18 head is more commonly used in my opinion but from what I've seen the b16 seems to make more power. I see you mentioned the word "budget". well a good b20/vtec set up doesn't cost a tremendous amount of money. heres what you will need:
1. b-series head (b16/b18)
2. b20 head gasket
3. oil lines and fittings
4. machine work on the head
5. a new b20 timing belt if using the b20 water pump.
or a gsr timing belt with a gsr water pump.
6. b-series motor mounts
7. b-series tranny, shift linkage, ecu, wiring harness and so on.
optional: (just to be safe)
8. new clutch
9. upgrade your valvetrain