It matters on any car, cat converter or not. The key is driving long enough for the exhaust to get hot and boil the water away. Short trips kill exhaust systems because the water pools up in the mufflers, mixes with acidic combustion byproducts, and rots out. I've been working out a lot of bugs in my '68 and not driving very far. I pulled one side of the exhaust to work on the trans and saw rust specks in the headers while water trickled out of the glasspack. I would say 10-15 miles minimum of steady driving is enough to dry it out.
Now that the science lesson is over, I will say that stainless or aluminized will be fine. Aluminized will last a long time if it gets hot enough to dry out and will save a lot of money. Stainless will take anything you can throw at it, but you'll have to throw more money at it.
If you get stainless, I would recommend having stainless cut-outs fabricated by a shop. All they need is are the flanges, a hole saw, a tubing notcher, and about 12-14" of straight stainless tube. The FlowTech "Race Readies" are mild steel and would look terrible patched into a stainless system