The B20b sleeves are weak due to the design.
If you decide on an Ls short block use forged internals like: eagle forged rods, cp forged pistons(9:5.1 CR), arp rod bolts, arp head studs, acl bearings, etc..
If you want a 2 liter and more insurance than just resleeve it to 84mm(b20b spec). Golden Eagle mfg.
The cheaper route would just be an whole Ls longblock. You could do the Ls/vtec but that involves more money. You can use the b16 head or you can use a b18c head(the b18c will yeild .3 higher comprssion, i think).
Ls oem rods and pistons are garbage when it comes to turbo setups.