Can one of the moderators switch this to The Boat Shed - might get more eyes on it?
sounds like you've got an exciting project and will build some great new family memories once you've achieved what you're after. Good luck.
Buying new provides comfort that you're not buying a lemon (pile of trouble = pile of dollars) but to get the benefits of new such as a guarantee you normally have to follow service regime prescribed by the retailer, which can be quite pricey.
Also, the dealer may specify they have to to fit the outboard or any guarantee would be null and void.
It might be worth trying to get a motor someone's traded in to a dealer with a good service history.
Look on The Boat Shed thread for discussions about motors. Some of the popular makes are Honda, Yamaha, Mercury, Suzuki, Evinrude and Tohatsu.
There are four strokes and two strokes in most size ranges, which is often a decision that involves noise, power, and economy.
As a starting point, 40-60hp would be the ball park (I have a similar sized tinny runabout and have a 40hp four stroke on it). Pushes it along nicely. But if I was regularly having a big mate on board, and dive gear, I'd have got a 60hp. Ditto having older kids on board with a biscuit, one or two hangers on mates, and the driver. 60hp sounds like it'd be required.
Also, get someone who knows about motors to ensure the length of the engine shaft is okay for your boat, which may be an older model.
For example, my dad got a new Yamaha for his 1970s boat, and had to modify the stern because of the length of the shaft.