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.
I’m 33 and I have been doing minor repairs since I can remember. Sewing buttons on or holes shut. Or making tiny clothes for barbies, looked awful, but worked. There are special ways of hand stitches for different purposes, but in most cases it’s a trial and error approach that in 90% of cases won’t end in “error”. You’ll figure out what feels better (like one yarn or double yarn) very fast.
But only at age 32 I invested in a cheap seam ripper. It always seemed excessive since you can basically just use sharp little scissors for that. I was wrong. I fucking love my seam ripper and I use it as a scissor now. This is so satisfying I would never ever let anyone rip any seam open for me. That’s the orgasm of sewing.
Also, you might want to use a threading aid (edit: is it called a needle threader?). Some thread is just a bitch.
Little side note: when choosing a thread to repair, try to go muted. If you have a green piece of clothing and a light green, dark green, and grey thread, very likely the grey thread will be the least noticeable, unless the green is the same shade. If in doubt go darker. For white thread I recommend going off white - unless you have a lot of white clothes, most of white stuff is off white (i.e. not crisp paper white). Some people say 100% cotton thread breaks easier than blend or polyester. So far I haven’t had any bad experience with cotton threats though.
Cotton thread is just objectively weaker than polyester thread, but I’ve never had that be an issue while sewing.
And in terms of the thread tearing when it’s sewn into a seam, sometimes that’s a feature, not a bug: sometimes it’s better to have the seam blow out and need to be resewn than for expensive or delicate fabric to tear. The right thread for the situation is always relative
I often do the opposite, pick a bright color that is not the color of the base material, to make the repair stand out more.
I do that too! But it depends on the repair. If I just fix a seam or a tiny hole in a shirt (you know, the ones that you need 2 stitches for) then it won’t stand out and look cool but just look out of place to me.
But I agree, in general visible mending is nicer and easier.