when i go to meineke or any shop, which type or brand of muffler should i ask for?

Ask a OEM replacement muffler. This a muffler that is as good or better than the original equipment (oem). Any reputable shop should be able to do this reasonably.

Being as your Acura is a 93 the 'newest muffler' shouldn't matter, it isn't fruit.
GL

I like the Morosco brand. Also there is a flowmaster but the Morosco has a lifetime warentee as opposed too 90 days for the Flowmaster. I have a Morosco on my ford f-150 pickup and it gives me the mellow tone that I wanted without being unbareably loud at freeway speeds.

Shops like Meineke and Midas offer a lifetime warranty on their mufflers, however the warrenty covers only the muffler. It does not cover the tail pipe, hangers, nuts, bolts, or labor. The best parts for your car, no matter which ones they may be, come from the dealer. They are designed to fit your car, not 50 or more other models. The problem with most aftermarket parts, is that they are made to fit too many different cars and don't fit any of them exactly. How long did the original muffler last? A replacement muffler from the dealer should last at least as long. It may be a little more expensive, but it will be worth it in the long run.