crapjumper, I’m doing exactly the same for my soon to be 13 year old. Bought the frame, got some Fox forks from classifieds for £145. I have all the other bits from his old bike & my spares stash.
I sold his old frame and forks for the costs of the new ones so I’ve budgeted about £100 for things like new BB, headset, gear cables, maybe grips etc.
I’d think that you should be able to get something half decent together running a 1 x 10 set up for £300 – £350 on top of the frame. Some smart purchases from classifieds, ebay and the usual facebook groups should see you with a nice bike.