With regards to the compressors, the CAT one will be quite significantly quieter than the dewalt one. Here’s a non-panel version of the same compressor, saves a few bucks, I don’t know if you wanted the panel for some reason.
1 gallon is just fine for single person trim nailing, or very short bursts of blowing things out. And they’re surprisingly small and easy to store and carry in that size, if you’ve seen the Ridgid cordless 1 gallon one or dewalt 1 gallon in store, that’ll give you an idea. WhIchever you go with, be sure to break it in as the manual specifies (usually something like running 10-15 minutes with the drain open so no pressure buildup), it will help extend the life of the compressor and reduce or prevent possible leaks in the pump. You’ll also need a hose for your nailer, this isn’t demanding so grab whatever floats your boat, rubber or plastic, coiled, etc. For such a small and quiet compressor, you’ll likely be working with it nearby, so one of the coiled hoses might be a good pairing. Also make sure to get the appropriate quick connect fittings for the hose and Teflon tape to put them on.
For the nailer, that’s a tricky and variable question. Oak trim has a higher tendency to split, though aligning the nail to the grain helps, I might go with the 18ga despite decreased holding power. MDF doesn’t split, but makes for nasty nail holes. Depending on the design and thickness of the trim, 16ga might split thin areas that 18ga does fine in. Door jamb should definitely be put up with larger nails or screws, while casing is less critical, same with baseboard. The main difference I note is how fast the trim works away from the wall. I’ve seen 10 year old houses where the trim is pulling away from the wall, or mainly held on by caulk that somehow hadn’t cracked and separated, and it’s because the stuff is held on with dinky little nails. Not saying for sure that would happen in your case obviously, but eventually all nails will loosen up somewhat. Laundry rooms may be slightly more prone to this issue, as the humidity rises and drops, the trim expands and contracts. If the walls (or trim piece) aren’t straight, 18ga will be less able to pull a bow into or out of the trim to follow the wall than a larger nail. I did a bathroom recently where the walls were so not straight replacing baseboard that I had to break out the 15ga just to get the holding power to bend the baseboard to match the wall. I’m not even sure how long that will last, we’ll probably be replacing it with screws in a few years.
18ga will likely hold just fine today if you don’t have to deal with those problems. 18ga leaves smaller holes to fill, can be used more cleanly in the smaller and thinner sections of trim, like the edge going into the jamb, and is less prone to splitting. 16ga will cause a larger hole, is more prone to splitting if there are delicate areas, but will have a bit more holding power than the 18ga. In either case, you’ll typically use the longest nail available for baseboard and the outside of casing, but maybe go a bit shorter for going into the jamb to prevent deflection and breaking through.
If I only had one single nailer, it would be the 16ga, and I’d have no hesitation putting up trim with it. I think you’ll find it more useful for more projects than an 18ga, and filling slightly larger nail holes on painted trim isn’t a huge deal. But the 18ga would be preferable if you are ever going to do any more delicate work, like rosettes or accents on trim (around here people like adding rope looking accent pieces) or crown moulding or similar where the smaller nail holes outweigh extra holding power. Or if you’re doing stain grade rather than painted, the nail fills are more obvious so a smaller nail hole might look a lot better. Door trim is really the main benefactor of the extra hold of a 16ga, since it’s always getting bumped into or held onto, or crazy people that put pull up bars on them, not realizing they’re held up by 4 or 5 18 gauge pins. Baseboard and window casing and crown moulding and the like don’t really get subject to the same abuse, which is why you can better get away with 18ga there. Trim head screws are actually really awesome, you could do the stuff that makes sense with an 18ga if that’s more your needs, and the difficult stuff or where you need some strength with screws. Online you’ll find a full mix of people that swear by 18ga, 16ga, 15ga, screws, glue (please no), hand driven nails, all for various reasons, and their applications from type of trim to squareness of house to ornateness I think drive some of the discrepancy.
Hopefully some other folks can chime in as well, i don’t want to be the only opinion here, I’m not a trim/finishing contractor that does this day in and day out. But I do enough sprucing up rooms for folks that usually involves replacing trim, sometimes to go more ornate, sometimes just to put fresh pieces up and do the corner miters a bit better than the original contractors, hopefully it helps a bit for your situation.