But how much is that? There is a minimum you are going to have to spend to get something that works reliably and wont frustrate them too much.
Working on the minimum investment I would go for either:
a used, not too old, taiwan made selmer copy, like an Antigua winds. $200-300 or less on ebay if you are patient, and $100 getting it checked out. I see a lot of Jupiters have changed hands for less than $200 recently. I dont have any experience with low end Jupiters, but the price is right. My taiwan made horn is an antigua 520, and its a decent copy of a Selmer SA80, with ribbed construction, high F# and a good tone. I got it for $200, although I was lucky and they are usually more than that.
One of the better quality inexpensive chinese horns, either used from someone you trust here, or new for a bit more money...something like the Gear4Music or Walstein horns that have gotten good reviews here. The problem with that is they mostly seem to be in the UK, so shipping is going to push your total cost up.
Either way I think if you spend much less than $300-400 including shipping and a check up, you are running the risk of not getting something that will do the job to an acceptable level, unless you get lucky. Even at that level of investment its buyer beware, so do your homework and take your time.
On the bright side, if they loose interest then you will be able to resell a used taiwan clone for much the same as you bought it, and that goes doubly for more expensive yamaha student horns like the YAS23 / 275 bought used in a private sale rather than from a music store.
But, if you buy from a store at least you know it should play right out of the box and will have some sort of recourse / warranty period if it doesnt. Unless the kids drop it of course..
Bottom line is that the sax is an expensive instrument...lots of moving parts and linkages that have to be just right, so if it looks too cheap to be true, it probably is.
Good Luck, I hope they take to it!