All you really need is a little plastic thing of needles ($1), some pins ($1), thread (varies but even good cotton thread isn’t that much), scissors (where you might actually consider investing a little - do not use these scissors for anything else, and consider a rotary cutter if you really get into it), and fabric.
Fabric might seem like the pricey part of the equation, but consider how much a thrift store is going to charge you for a duvet or a pile of t-shirts! I have something like 30 t-shirts I spent maybe $5 on several months ago, and I’ve been working through that pile for a while.
You can turn a t-shirt into a pillow, a reusable bag, use the scraps to patch clothing, make dolls, quilts… The bits that get to be so small to be unusable for a scrap quilt you can use to stuff things.
It takes a lot of time compared to machine sewing, but it’s an activity that can be done while watching a tv show.
Seconding someone’s advice that kits are a bit rubbish. The only things you need are needle and thread. Start with a multi pack of needles, and observe how they’re different. Different needles may differ by: the thickness of the needle; whether the tip is sharp or blunt; how large the eye of the needle is; how long the needle is. Different needles will have different roles, but it’s so easy to get bogged down in complexity, so just get an assortment and discover as you go. Part of learning is building tacit knowledge around what the right tool for the job is, so just give it a try and feel free to try other needles to see how they feel. Personal preference matters…
My main advice on hand sewing needles is to invest in high quality ones, because they’re much nicer to use and last longer. For perspective on what counts as “high quality”, my current ones that are my favourite cost me £4.20 for a pack of 6. That’s expensive compared to a supermarket multi pack, but not excessively so. These ones were particularly fancy, by my standards (Clover Black Gold), but they’re a useful benchmark as being about as fancy as you can really get. John James is another good brand. If these aren’t readily available where you are, don’t sweat it — just use this as a benchmark to see what the rough equivalent is where you are.
A pin cushion is useful for storing needles temporarily, but you don’t need to buy this. You can make one as an early project with some small swatches of fabric and some scrap paper stuffing.
I strongly recommend a thimble for anyone who is going to do significant amounts of hand sewing, because it makes it much easier to build a rhythm and sew neat and fast. It feels clunky at first, but once you practice, it makes things far quicker and easier. Unfortunately, most people’s experience of thimbles is of ill-fitting ones that probably came in some kit. You need one that fits comfortably on your middle finger without falling off or squeezing too right. A simple metal thimble will do, and they’re cheap, but it can be a faff to find the right size. The sizing is sort of standardized, and usually printed/engraved/debossed on the thimble, so you can use that to ballpark if you have some ill-fitting thimbles around. Otherwise, it’s best to go to a craft store and try poking your finger in some thimbles to find one that fits.
I don’t have good recommendations about thread. I got started using generic machine sewing thread, which you’re not meant to do, because it’s worse and harder to use. I find it hard to tell though, because by the time that I got specific hand sewing thread, I had enough skill that I had my own snobbish preferences and specific projects requirements. You don’t need a multipack of thread though, because that’ll be more likely to be crappy. Pick a colour that matches most of the stuff you wear/will be repairing (for me, it’s black). Also get some thread in a contrasting colour, because sometimes that’s useful (such as for temporary lines of stitching). You probably want some cotton thread, and also some polyester thread. In general, repair like with like: so polyester thread for synthetics, and cotton thread for cotton or other naturals. Beeswax can be nice for reducing the friction of the thread, but that’s not super necessary.
I worry that my advice may overcomplicate things, when that’s the opposite of what I want to convey. If there’s any recommendation I could give you, it’s to just get something and start. Hell, if you feel overwhelmed by how granular this is and are at risk of not diving in, then go for a kit if it helps — just don’t spend too much and know that the lesser quality will give you a worse experience. However, the most important thing is to just get started. You can upgrade your stuff or buy specifics as and when you need them, or you feel you’ve outgrown your existing tools.
You will botch repairs and need to redo them. Sometimes you will make it worse than what you started with, but that’s part of learning. However, the sooner that you start to tackle the simpler repairs, the sooner you’ll have the proficiency to be making all sorts of repairs and alterations. I give you this advice as someone who accidentally became proficient in sewing: I dove in and spent a long time being mediocre, and I still feel mediocre at it, but people regard me as being quite skilled. There’s no cheat code, but to take at crack at it.
This is terrifically detailed and actually not intimidating at all. I really appreciate your perspective on how to get started (now) and it’s helpful to have a reference for brands and quality of needles. I think these are some of the things that have been holding me back, but now I feel like I can take that first step. Thank you for taking the time to write this all up, and thanks everyone for all of your input!