I like Wilson junior rackets. They vary in price from cheap to very expensive, but at his age the cheap will be fine. And they've usually got reasonable cases, which (usually) stops damage in transit.
I think 17" would be better if he's just 4yo. My nearly 6yo has just moved into a 21" (from 19") but at that age if they're too big then they find them very hard to use as the head is the heavy bit at first. If he's tall and has large hands (the grip is bigger too) then he may be fine with the 19".
If you have a large Tesco, then some of them have rackets, although I don't think they go as small as 17". You could take him to see how well they fit.
Alternatively contact the coach and ask if he could borrow a racket for the first session and use that for the coach to recommend which size.