I don't know about price, but the H23A option is not bad. You'll need a mounting kit from HASport, Place Racing, or HCP to do the conversion. I'd certainly do this before rebuilding your current engine (the burning oil problem is probably due to a problem in the cylinder head, and you'd be better off just replacing the entire head, rather than trying to fix the existing head).
However, I'd also think about doing a compression check in your cylinders. Get a Helms manual for your car, or through another source find out what the cylinder pressure should be for your cylinders. If you haven't seen drastic pressure drops in any of your cylinders, or if there are no gaping inequalities in cylinder pressure from cylinder to cylinder, I'd consider just getting a different head. I'm not positive, but a VTEC B series head should be able to bolt right onto your block - you should just get one from the same generation for ease of adaption for the ECU's. A B16A head would probably be a good choice. And you can probably get one for your car's generation for $400 to $500, maybe even less.
Now, if you want to do a forced induction set-up for your car, and you will need rebuilding no matter what engine you choose in order to run with this, than scratch getting an H23A. I'd keep what you have and work with it, since you'll have a good deal of displacement to work with.
I hope this helps, and please post again if you have more questions we can help you with.