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 was going to advocate machines, specifically the vintage Singer machines (the black, all-metal dudes). They are very simple, there’s tonnes of information online for repairing & maintaining them, and you can usually find people just trying to get rid of them. Find one that isn’t rusty and moves freely and you’ll probably just need to oil it and mess with the tension.
If space is a concern, you don’t need to keep it in the sewing table (though it’s more comfortable). Those vintage machines are simple and tough to kill.