I also have a '90 teg going for motor swap. If you want 0 headaches, do a b20 - the b20z being the best, but most expensive. It's a direct drop-in, if you make sure it's obd0. Get the ecu, too. It plugs right in - no joke. Your other easy options..

1. b16a or b18c with a pr3 or pw0 ecu: To do this, you will need to run 4 wires into the engine bay - knock sensor and three vtec wires. Aside from that, total drag and drop operation. google "integra xsi" and you'll see why.
2. ls/vtec: This setup is almost the same as the first, but there is the issue of the knock sensor. Either, you need to find a blank spot in the block, drill and tap to instert one.. or you need to disable it. This is easy with hondata systems, but hondata is obd1 only. Since we're obd0, you would need a chipped ecu with disabled knock sensor. This is not all that tough. If you want, visit moates.net and get an ecu chipped for yourself. You can send them your ecu (pr4 obd0 - don't get confused.. there is a pr4 obd1, as well) and let them know you want it converted to vtec (yes, they can do that) and chipped with a pr3 bin flashed onto it. This also involves some machining of the head OR a vtec conversion kit from golden eagle manufacturing. Then, you need to find a complete b series vtec head (b16, b17, b18c) and pw0 or pr3 ecu and strap it on.
3. If you're REALLY ambitious, you could do an h22a swap, but that involves an obd1 conversion and lots of cash spent on hondata or place racing mounts.

That rounds it out, essentially. In my opinion, the b20 is NOT the way to go, as it's a lot of work for ~15 horsepower. For the same ammount of work, plus running 4 wires, you get so much more. Keep in mind, though, option 1 will net you between 160 and 200 hp to the crank depending on how much money you want to drop. Option 2 gets you 200-225 at the crank due to the magical combination of the ls block's sick torque plus the upper rpm muscle of a vtec head. Just don't run too hot for too long, as the b18a block has no oil squirters inside like a vtec block. Option 3 is an advanced swap. Personally, I'm going for option 2. Hope this all helps.