Cheap and fast is not reliable
Reliable and cheap is not fast
Lastly, Fast and reliable is not cheap.
Ls/vtec's can be reliable as long as you build it properly ie, ARP rod bolts, ARP/Golden Eagle head studs, Golden Eagle vtec conversion kit would be a good start for an ls/vtec.
You could also do a B20/vtec which is essentially the same but with a B20 block.
A GSR motor would be a good choice, so would a type R motor.
But I would NEVER get a B16 motor for an Integra. B16's have no torque what-so-ever.
As for if you do decide to turbo, get a good reputable kit such as drag and revhard [no e-bay/ssautochrome kits, they are known to break and have many issues]
If you do decide to get a vtec motor and turbo it, you won't have any issues as long as its tuned correctly. People say ls motors are better for boost because they have a lower compression ratio but in reality it is not better, just safer.
Higher compression like of a GSR or Type R is better for making power due to the fact that when you turbo or supercharge you are raising you static compression ratio.
A stock GSR motor with your average t3/t4 turbo on about 9-10 pounds of boost and a very good tune can easily see about 300whp while still being reliable.