I would ditch buying an used engine and dropping it in right away, if you really want reliability... buy the used engine and rebuild it. It will give you maximum performance and mpg. For the transmission, it might also need a fresh rebuild (around $200 in parts). If your car doesn't have the original transmission, it is very likely that they swapped out the hubs. Which will make it a pain hunting down some unless you get a whole HF donor car..
If you do the whole work yourself. It will probably come to be:
used engine: $200
engine rebuild kit:$~300
trans rebuild:$~200
Shell:400~800 depending on condition
so if you pay full price for everything, it should come out to around ~$1500...
if you want a shop to do it, and u don't want to do it yourself... throw 2k out the window, and start thinking about $4k and up..

 

I would rather find an HF that maybe has some cosmetic issues and try to restore it. One significant downside to trying to rebuild an HF is that the parts to rebuild the engine, namely the bearings, are very hard to come across.

But to answer your question, I would expect to pay $200-300 to ship an engine and $500-800 for a shop to put it in. Of course any time you get into swapping engines and transmissions you run into hidden costs, even when it's stock for stock.

 

Might be easier to source a civic vx engine and use the intake mani and wire harness with sensors for the hf with the hf ecu....

 

Thank you so much for the info. I found a "HF" in my state for a good price as a recondition candidate. Im not sure if it is an HF as he has said. Theres a moonroof but that can always be aftermarket. I cant see the HF on the back of the car with the fuzzy picture however there is no rear wiper blade but a dark spot where one could possibly be attached.

For a 91 HF the vin is: JHMED8351M5008181
But from IDing it by the vin i believe the 8th digit has to be a 6 for CRX so something is off?

He gave me this good picture of the engine if anyone could identify that its an HF engine for me. IMG'ing the picture would be to big for a forum so here is link:
http://i177.photobucket.com/albums/w227/robert-0137/DSCF5803.jpg

 

That is a DX that has been molested and beaten (you can assume beaten any time you see a header and intake swap). 835 in the VIN is manual DX, 845 is auto DX, 836 is HF, and 936 is Si.

Mike