Always choose better quality. What looks new and comfortable, looks nice, but especially if you're traveling with a small child, the older types of monohulls, with handholds everywhere, and easy to put netting on. They are, imo, safer than the newer, more flash yachts, due to differences in the construction techniques.
You'll need a spot where you can quarantine your daughter where she will be safe, when both of you adults will have to be on deck
together. You'll have to teach her to stay there till you come get her. The "terrible twos" don't last forever, and she will become more amenable to instruction *soon*.
It will depend on the vessel you choose, of course, but IMO, you have not enough planned for upgrades, so you may have to lower your purchase price
expectations, to provide for the upgrades.