Go for the ukulele! Pennywhistles are also great if you want a cheap musical instrument - you can get them starting around $10 USD. And no one will ask you to sing while playing one if you're worried about that....
I highly recommend a jam group if you can find one. Either a ukulele group or one open to all instruments. Someone in most groups will probably have a ukulele that you might be able to noodle on for a little bit to get a first feel of it, and they can give you some pointers. Casual musicians and especially those in most jam groups are usually pretty generous with time, info, etc. (At least that's been my experience, though the group I'm in was also started by a teacher with the goal of her students having a place to play.) The trouble is finding the jam groups, as they're often run by an older crowd that doesn't have much of an online presence. Facebook might be a good resource for finding jams. In my area, at least, once you find one group they'll be able to tell you about many of the other local music groups.
I sort of took piano lessons in grade school and my mom plays fairly well. I picked up ukulele somewhere in high school, and with chord charts and a little YouTube I was happy enough without ever taking lessons. Personally, I would look up lots of YouTube tutorials before I decided whether to buy a $30 book. Now my main instrument is a hammered dulcimer, which is a lot of fun but neither cheap nor very portable....
For getting a ukulele, I'll second ebay, Craigslist, Facebook marketplace, Nextdoor, and the library if you can find one with instruments. I have a Rogue baritone ukulele that my sister bought used off of a college student who had just finished a music class. It's a cheap brand but has worked well enough for me. I think I've replaced the strings once, but they worked fine for a few years. Here are a bunch of that brand listed on ebay:
https://www.ebay.com/b/Rogue-Ukuleles/16224/bn_7428811?
I agree clip-on tuners are nice and fairly cheap, but if you have a smartphone you can also download plenty of free tuner apps. I use Pano Tuner:
https://play.google.com/store/apps/details?id=com.soundlim.panotuner
Regarding tuning ... Some form of GCEA is standard. Sopranos, which are the most common size by far, will have reentrant tuning, where the G is a 5th higher than the C, so your highest-pitched two strings are the outermost ones. Same for Concert size. Wikipedia (
https://en.wikipedia.org/wiki/Ukulele, see Size and range section) reports that tenor ukes can have that string either higher or lower. Baritone ukes, which is what I have, are tuned DGBE, no reentrant tuning, like the highest 4 strings on a guitar. Those are more or less the standard 4 sizes with the other 3 sizes listed on Wikipedia's chart being much less common. One of these years, I'll probably pick up a soprano for portability, but it hasn't happened yet....
