Should I swap it or rebuild it?

Some Mazda owners have found it cheaper to replace the engine when it came time to do the water pump and timing belt. So a swap is cheaper.

However, at 180K miles more then likely the engine does not need a rebuild. Do a compression check on the engine. If that proves me wrong, pull the head and check out the cylinder walls and the head itself.

The glitch in your plans is modification. There are two routes to take-

1. Forced induction

2. High compression

Do not attempt both! If you plan on forced induction and stay mild in boost a low mileage used engine should work. But if you plan to go over 10 lbs in boost engine work will be needed and this can run into bucks in addition to the cost of which ever method you use for forced induction.

If you go high compression, it still will require a lot of machine shop work and be expensive.

From the point of view of what is best route to take, a larger engine from a newer Miata with the ECM and wiring harness is a good investment. 96 or latter because the ECM gets input from a knock sensor. If you don't want to use a stock ECM at least consider a 1800 engine and use Mega Squirt.

One last thing, consider a rear end swap. Unless the transmission is bad, this is almost required for a modified engine. The stock ones in a 90 don't take abuse (hard launches) very well. While the transmissions are much the same across the board (at least for the five speeds).

In terms of transmission. Swapping is cheaper. They are very complex and labor hours are very long for rebuilding transmissions. Most mechanics don't even do it. They replace it instead.

In terms of engines, rebuilding is cheaper. Less than half the cost of getting another engine.

Take a look at the BPT engine. It is a popular swap for older Mazda's with 170HP turbocharged engine. But that engine (used) costs $2000 by itself.