Your handling will suffer regardless of wether you go with a b or h series. That is what aftermarket suspension is for. The h weighs roughly 40lbs more than a b total(engine and trans.). You can turbo an ls and handle better and beat stock h22 civics all day for cheaper. But when the h22 starts seeing even bolt-on mods, the cars will be even. Turbo an h22, and the ls is seeing tailights all day. The h22 swap is fine for dd when it comes to handling, but you will suffer going around a track. You also won't be able to keep a/c and p/s, so keep that in mind.
If you wanna get real spendy, get a k-series. You won't even need any FI and you'll be faster than a turbo ls, and almost even with an h22 with bolt-ons.
There are positives and negatives to any swap/build you do. It all depends on what you think is best.