Engine choice is really up to you and depends on what type of goals you have.
Many routes/directions to go between choosing a B, H, or K series? You'll run into complications with some, Like special mounts for the K or H.
The Type-r engines run such a high compression they're not real good for turbo's though.
Transparent is right, you should really search through all the options and find your own pro's and con's to each swap. I got dial-up and it ain't killing me , besides you don't plan on ordering the motor tonigh (I hope).
There is complete sites dedicated just to Hybrids (swapped cars). Take your time to plan and think things out. It sounds like you got a budget and that's a good thing, just work around that. If you need a few pointers or got a few questions PM me cause I'm in the middle of a swap currently.
Good luck