For a guy, I have small hands, plus arthritis. Guitar selection can be an important factor. I would look for a guitar with a slender neck, what I call for me as more "playable" with my aging hands and fingers. I do the same when looking for a new bass. They are not all created equal and there are a number of decent guitars out there that are very playable for people with hands like ours. The difference may not seem like a lot, but you'd be surprised how much a fraction of an inch can make. Action (the distance of the strings from the neck) is another factor. On just about any decent guitar the action can be adjusted. Two acoustic guitars with necks and actions suitable for smaller hands are the Taylor 110 and the Alvarez MD 90. I found the Alvarez to be slightly better of the two. Classical acoustic guitars all have wide necks so stick with the steel stringed acoustics. Electric guitars tend to have better necks and actions. In any case, go to a music store with a large inventory and try a bunch to see what feels the most comfortable for you, as well as what fits your budget. Note that guitars with the better necks and actions will not be the inexpensive starter models, but you can still get something decent for less than most of the more expensive models from the same company. Also, don't rule out a bass guitar. The 5-strings are popular these days, but I stick to the traditional 4-strings.
A mandolin really doesn't fit into any rock style of music.