I've recommended it to a few people before but the 11'6 Fanatic Ray Air would be a good mix, i think it's a cracking starter board. It's 11'6 long so a little bit of extra length to help glide and a pointed nose and only 31" wide to aid tracking for going in a straight line. It's also not too long that it becomes difficult to turn. As a note, i did have myself and my mother in law on the board together in Spain, whilst i'm not saying it coped perfectly, it wasn't completely unusable given it had 2 adults on with a combined weight around 160kg so you and your kid combined are only likely to be the same as me on my own!
It's only downside is that it's single skin so not quite as stiff as higher level boards, but it's still stiff enough for me at ~100kg to not notice too much in the way of flex, and that was when using it on a choppy sea, on flat water it's pretty solid. That's the trade off for them hitting that <£500 price point i guess.
I don't think i've seen you mention it but have you got a budget in mind?