Oh, and interesting tidbit - trade posts claimed in war do not check your trade post cap (they still add to it, but they don't care if you're over or under it when you declare the war.) Fun CK2 Moment if you manage to make it to King or Empire level: Create and grant independence to a new Merchant Republic. County claims are a little trickier, but not by a ton.
Wouldn't be surprised if it got nerfed.) In the meantime use mercenary armies to pick off targets of opportunity and expand as you can it's not hard to win city-claim wars when you can drop a mercenary army on somebody and siege out the city without having to worry too much about the rest of the province. You can also use/abuse the fact that trade posts count toward your holdings count, and thus toward your retinue cap, to have a bigger retinue than basically everybody (at least, they did last time I played a Republic.
The Palace becomes a very, very rich source of both troops and cash, as well as providing neat personal benefits to your future rulers. If you have the patience, spend a ruler or two focusing on your family palace + upgrading the capital holdings in your republic.