I don't have a VX (but have three '91 Civics) and don't know all the specifics with their transmissions, but if you've done swaps before and the rest of the car is to your liking, I'd personally take a chance and figure out the tranny details later (since you're in a hurry). There are plenty of other posts on this site, and a few experienced people, to give you those answers.
A Civic 5sp is a lot lighter than a RWD camaro trans for sure. I did the clutch myself on an older Honda with no problem. The gearing on the VX is different so you'd want to find another VX trans, or maybe you can salvage whatever is different (final drive maybe?) from the "bad" transmission and swap into another Civic transmission. Again, ask the VX guys on this forum for the details later.
Replacing the transmission on a VX is pretty similar to replacing a transmission on a Camaro. The primary difference is that on the VX their are 2 half shafts which come out to each of the front wheels. You have to pull the front wheels and a little disassembly of the front hubs, to get the half shafts out, but it is basically doing the same thing as taking out the drive line on the Camaro.
After that, it is pretty similar.
As far as replacement transmissions go, you can use anything from 92-95, but the VX and CX had a lower gearing setup on most of the gears and the differential assembly. Consequently, if your looking for mileage, you need to get a VX or CX transmission, or have the existing one fixed.
The biggest caution would be don't take it to a shop and ask them to give you a replacement. They will often just get a generic rebuilt unit, which physically looks the same, but which will probably not have the high mileage gearing the current transmission has.
I replaced my vx tranny with one from a junk yard, I had never done a tranny before and it took me about 8 hours in total, and I needed a 2nd person for about 10 minutes to help me get the new one lined up perfectly, ended up replacing the axle seals at the same time, along with a new clutch and taking the fly wheel to a machine shop, the whole job cost me about $300 for the seals, axle 'c' clips, clutch, fly wheel work and tranny after the core charge and could have been done faster if I had done work like that before.
sounds like a FWD tranny isn't all that bad afterall.
I would MUCH rather replace a Honda transmission than a RWD transmission ANY DAY! I HATE replacing RWD transmissions. FWD transmissions are SO much easier due to the fact that you have easy access and unlimited clearance on the top side of the transmission. You can literally just pick it up from the top and stab it that way - no need to worry about transmission tunnel clearance or trying to squeeze under the car.