Along with your first ukulele, you will probably want a few other things. None of them is particularly necessary; you can play your uke without any of them, but some accessories will make it easier and better for you.
Item one, a case or gig bag. Even if you never take your ukulele anywhere (and why wouldn’t you?), your household might contain kids or pets an instrument should be protected against.
There are hard shell cases, which provide the best protection but are heavy and expensive. There are rigid foam cases, less protective, lighter, cheaper. There are gig bags or soft cases, minimally protective, lightest, cheapest.
I wouldn’t check a uke on an airplane without a hard shell case. Not that I’ve ever checked a uke on an airplane. They do fit in overhead racks pretty well. For not too stressful travels and home environments a good padded gig bag works well enough. But my two best ukes do have rigid foam cases, brand name Uke Crazy (from Kala, I’m pretty sure). They each have an internal compartment, an external compartment, and a strap for carrying. They’re both basic black. So are the gig bags for my concert (which came with it) and sopranino (from Caramel). You can get cases and gig bags in fun colors and prints… for a price. (My Phitz baritone soft case is blue.) Or you can make a gig bag, if you’re into that sort of thing.
If you have a tenor ukulele you need a tenor ukulele size case or bag, of course, and likewise for other sizes. But even among tenor ukuleles there’s some variation in size, and what that means is, if you’re buying online, you need to either check with someone who knows whether a xxx case will fit your yyy ukulele, or be prepared to find out it doesn’t and you need to return it. Gig bags are probably less likely to suffer this problem, being non rigid, but there are no guarantees.
This time I mean the electronic device to assist in putting your ukulele in tune. You can get away without one. If you’re not playing with anyone else you can just put one string at what sounds like a reasonable pitch — obviously requiring a certain amount of experience — and tune the other three strings to that. No one will get upset at you for playing solo in D quarter flat tuning. Or, if you want to be at a specific absolute pitch, you can compare against an instrument known to be in tune, if you have one; there also are tuner smartphone apps available. But a clip on tuner is inexpensive, easy to use, and very handy. Because it hears vibrations through contact rather than through the air, you can use one to tune up while all around you are playing and talking. Of the two I have I like one better because of its clear and bright display; the one down side is it has only ukulele and chromatic modes so is harder to use for tuning a baritone ukulele. For that I prefer my other tuner, which has a guitar mode — baritones are tuned like the first four strings of a guitar, so that works. I haven’t named names here because the tuners I have aren’t on the market any more and my comments don’t really apply to their successors, but some good brand names are Kala, Lanikai, Fishman, Snark, Korg, and Planet Waves.
The batteries on these wear out eventually, so toss some spares in that case pocket, and for heaven’s sake don’t buy them at a drugstore or a mall watch repair booth that’ll soak you for five dollars each. Look around online for battery packs of 5 or so for a similar price or even less. (And look around for advice on avoiding counterfeit batteries, because there’s a lot of them.)
A wood, acoustic, soprano uke is a lot smaller and lighter than a guitar. Traditionally it’s played more or less hugged to the chest with the right forearm, and if that works for you, do it. Some people find this awkward, especially with larger and heavier ukuleles, more so with ones that have geared tuners and a correspondingly greater tendency for the head to sag if the left hand isn’t constantly supporting it. I prefer a lower playing position, with the right arm more relaxed and neither hand trying to support the instrument and play at the same time. So I usually use a strap.
Few ukes come with strap buttons installed. They’re cheap to buy, though, and easy to put on. Your music store will do it for you, or you can do it yourself if you have the nerve to take a drill to your uke. You can put one button on the tail and one on or near the heel of the neck, and use a guitar strap with button holes on both ends. Or you can just put one on the tail and use a strap with laces on one end which tie around the headstock. (My preference, for support at the head.) Then there are straps made for ukuleles that don’t require buttons. Some fasten around the waist of the uke body and others hook into the sound hole.
Propping your song sheets up on a chair gets old quickly, and a folding music stand can be yours for under ten bucks. These are lightweight and compact, which is good for carrying, but not so good if you’re dealing with large heavy music books under which they tend to fall over easily. The groups I play with make use of the Daily Ukulele book and a locally produced book of songs both of which are a couple hundred pages, so I’ve moved beyond these stands. For transport I have a stand made by Hamilton and rebranded Stage Rocker. The legs fold up and the rigid desk detaches, and I got a bag to transport it in. It’s kind of a pain to carry around, but it’s way more sturdy and stable than a lightweight folding stand. Also you can get accessories like a drink holder that’ll mount on the post, which in our more beer-oriented group prevents a lot of spills. For home I have a Manhasset stand, not very portable but very sturdy. Manhassets are the standard stands, if you will; if you ever were in the band in school, you probably used Manhassets. They’re also not cheap. Unless you get them used from someone moving to Mexico.
If your uke came with decent strings, they shouldn’t need changing for… well, a while. Some people like to change strings every few months. Some let them stay on for years. It depends on how sensitive your ears and fingers are to their rate of degradation. Or, of course, on how much you want to try different strings to find some you like. I’m not much of a string changer myself; I have an extra set or two around in case of emergency but emergency string changes are pretty rare.
Particularly if you have a solid wood (not laminate) uke, you should take care it doesn’t get dried out in low humidity conditions. The number I’ve heard to stay above is 45%, though I don’t think there’s anything especially hard and fast about that. If you live in a warm and humid environment, or if you have an effective whole-house or room humidifier, that may not be a problem. In the winter in Syracuse, outside the basement, it is. If there’s a question, invest in a good hygrometer to be sure. Emphasis on “good”. I’ve found a lot of low cost hygrometers, including ones specifically marketed to owners of reptiles and wood clarinets (both of which can suffer expensive and heartbreaking deaths if subjected to the wrong humidity), are completely unreliable. If you can’t keep your ukes’ environment above 45%, you can build or adapt a cabinet to be a higher humidity storage area. Or you can keep your ukes in their cases and get a low cost case humidifier to keep the inside the case humidified — or you can make one.