The difference between Basic and non basic tickets is all about checked luggage, but as you surmise, there is an impact on seating options too.

With the more expensive ticket, you do not get free seating but (a) you can purchase a seat and (b) you may be able to select seats at 48 hours rather than 24 hours and (c) at Online Check-in you can select usually from multiple options and without cost. If (b) applies, it should say so on one of the early screens.

With Basic you can do (a) but not (b) or (c). At OLCI you will be given a seat and can't change it without paying.

Seating is cheaper if done at the time of original purchase, it gets more expensive if you leave it. It's also important to stay on one PNR (reservation) because something like Theoretical Seating (TS) will actually keep the two of you together anyway, regardless of (a), (b) or (c). So BA is different from those airlines that deliberately split up couples and families in order to drive more revenue. Mostly TS works but it's not guaranteed.

Therefore if seat selection is a big deal, then you should add the cost of it to the total ticket price and shop around to see if you get a better deal. You can find out the seat fee by advancing slightly further into the dummy purchase process since after selecting flights a seat selection window should pop up, On the other hand, if you can get Ruby status on any oneworld airline (including Alaska and AA) then you get free seat selection at one week to departure. That applies to both Basic and non basic tickets. If your daughter is under about 12 years old then she has to sit next to you (in the unlikely event of TS failing).