Having more male family members increase your trade post limit though, which is very important for expansion. I always wanted my family to breed more, even paying dowries to get them wed. Having to pay them a share isn't so bad, since they're unlikely to marry matrilinealy - so most of that money is staying within your family, more or less.
Other republic tips... Your mansion gives good stat bonuses and a reliable income/levy, and can never be lost. The upgrades take a long time though, so start early if possible. The most useful but expensive is the size upgrade, which increases your all-important trade post limit (and unlocks the other upgrades).
You probably want to win every election. It's not really hard, since you basically know ahead of time how much money you need to spend on the election. However, there is a small random factor, so try to overshoot some. The election is strongly based on age and prestige, so killing off the patrician of a rival house can make their electability plummet. That wasn't usually necessary in my case though.
You can expand by placing a trade post, which lets you declare war for a city there. Once you hold the city, you're allowed to declare war for the county. But it's expensive to place trade posts in places where the ruler hates you, and they'll likely try to destroy it for gold. If you can beat their army, that's not a problem.
You get a percentage bonus to trade when you control contiguous sea tiles. That's what the "trade bonus" upgrade at trade posts is upgrading.