I went to one violin lesson when I was 8, and small and skinny for my age. I found the method of holding it uncomfortable, and never went back. If those are the only two options, I'd recommend guitar, since it's more of a fine-motor instrument, and you don't have to support the weight.
I recommend you avoid the mistake we made, and get a quality instrument. We bought DD a cheap, kid-sized classical guitar, because we didn't want to spend the money if it would be a short-term interest she drops. Well, it turned out that the poor quality of the instrument was a major reason WHY she dropped it... where's the reward in playing music if it doesn't sound good? Each fret down the neck would be further off key than the one above it, so it was impossible to play anything in tune, and there was nothing that could be adjusted to correct it. We've since remedied it by buying her a high-quality instrument (we didn't break the bank, but by this point I knew what I was looking for), and she still picks it up from time to time and goofs around, but she has yet to recapture that previous passion.
In your case I'd also recommend an instrument with low action (action is how high the string hangs over the neck), which would pretty much rule out a classical guitar. Low action means less hand strength needed to press down a string.
To give a ballpark estimate, our DD's acoustic/electric would probably meet your DS's needs. We found it for about $230. It comes with a built-in electronic tuner, which is great for her.
I think your bigger problem here, depending on the nature of it, is the vision issue, because that's going to make reading music more difficult. That could be another point in favor of the guitar, because tablatures.
