How old is he? (ie is he a teen who’ll need a full size guitar, or a 9 year old who may need a 3/4 size?)
Acoustic guitars don’t actually need to be very expensive for a beginner - of course you do get what you pay for, but the beginner level ones are totally fine to start with.
I would be inclined to get a “beginner” one from an actual proper music / guitar shop, rather than from Amazon or online. Any chance you could get to one for him to try them?
Something like this place: https://www.andertons.co.uk/browse/best-for-beginners/best-acoustic-guitars-for-beginners/
or
https://www.guitarguitar.co.uk/guitars/acoustic/beginners/
Have a look at those sites. But it’s almost certainly true that you’d get better value second hand. The strings being messy isn’t a problem at all imo. That’s just someone has strung it themselves like you do, and it’s less tidy looking than a shop one. You may need to get new strings anyway at some point - they’re pretty cheap.
I wouldn’t buy a second hand one through the post - I’d look on local marketplace and see if someone is selling one. It’s likely to be a beginner ish one, so you may be able to compare prices of what they’re selling with the models on the sites I linked.
I think second hand acoustic guitars are generally fairly safe. They’re not that complicated an instrument (I speak out of love as an acoustic guitar player - you can get absolutely beautiful better quality guitars, but for a total beginner a cheap one isn’t terrible).
edited to add, after browsing our local marketplace:
Don’t bother looking at second hand ones that are noticeably scuffed or with massive big scratches or dents in them. Or if they say “one tuning peg broken but easily fixable” or something like that. But apart from that they’re probably ok!