firstly, congratulate your son for choosing a skateboard and not a stupid scooter. tell him from me… ‘good man!’
ok, first question, what sort of skating will he be doing because if its skating in skateparks then you need a different set up to just cruising around the street.
so lets assume the club are teaching him to skate transitions and, for want of a better way to describe it, trick skating. for this you need a conventional looking board, double kick and small hard wheels. but thats the easy bit.
your kids height hugely comes into play but if you say he’s roughly the height of a 10 year old, and definitely with your budget, then you can at a push (pun intended) get away with a regular board in terms of lengtn (about 32″) and wheelbase (about 14.5″). width here will be the key and i’ll come onto that in a sec.
the prob with putting a small kid on a full size board is that the stance becomes too wide, for a younger/smaller kid you really need to look for kids boards and for anyone reading if you can find them darkstar make the best cheap kids completes.
but getting back to full size, the main thing you need to look at is width. decks these days have gone wider, 8.5″ etc but a smaller footed kid needs a narrow deck for control, massively so when they start learning to ollie and then kickflips etc. at the max 7.75 but less if you can for smaller feet. my son is a very good skater, aged 14 uk8 shoes and has only just recently gone to an 8″ deck.
if you are buying a complete you dont need to worry about trick width, but 129 are what you should have, and wheels down around 53mm no more.
i’ll do some links in a sec to completes, but there is a massive world of difference between a cheapo (event at 50-60quid) and a decent board. to be honest you would be better buying a cheap deck, cheap wheels, cheap bearings (skate bearings are just a standard bearing, look on ebay) and some good independent 129 trucks (pop some good soft bushings in, bones hardcore soft ideally) as the trucks will last you for years (my son is riding a ratted out set that i skated myself 10 years ago, they last).