I'm a pretty minimal sewist, but here's what I consider essential:

• Needles - I prefer to have some "short and sharp" and some "long and sharp" ones on hand. I am genuinely terrible at remembering the different sizes/numbers and end up eyeballing them when I shop.
• Thread - The one and only area where I don't use secondhand, because thread can break down over time and old thread tends to break easily.
• Pins - I like the metal ones with the little colored glass bits on the top so I don't lose them as easily. I use pins because I only have two hands. Since I'm hand sewing, I can put as many pins as I want in the fiddly bits and I don't have to worry about damaging a machine needle.
• Tiny scissors - I have a million pairs of scissors and they all disappear when I need one, so having a pair that lives in the sewing kit is essential for me.
• Fabric scissors - These don't travel but it's important to have good scissors when you're cutting fabric. No really, it is. You can get some nice ones secondhand but you may need to sharpen them... or you can get them new with one of those 60% OFF coupons from Michaels or Joanns.
• Beeswax - To keep the thread from knotting up too badly. You can get them in cute shapes or in little holders so they don't get as fuzzy.
• Thimble - I didn't realize for many years that thimbles came in different sizes and fit mattered. Don't be like me. Find a thimble that fits, and actually use it.

And then the other things I consider really nice to have:

• Measuring tape or a ruler? Well, you see, I sew like I cook... which is to say I look at a couple of patterns and then make it up as I go. Sometimes it's convenient to have a mesuring tape handy, and I probably should use it more often than I do... but I don't.
• Safety pins are good to have sometimes even if you have plenty of regular pins handy. Plus they can make a pretty decent bodkin replacement in a pinch.
• Of course, having a bodkin would be nice too. That's the tool you use to thread a cord through a tube to make a drawstring or put in elastic.
• I have a lovely, wood-handled seam ripper that I got at a trunk show. Do I need it? No, not really. But it's comfortable to hold and makes me smile when I use it.
• I don't actually have a lovely little sewing bird, but I've been obsessed with them for ages and I really ought to get one, it seems super useful for holding stuff.

Hand Sewing Tutorial (Right Handed): Backstitch: Backstitching is probably the single most useful stitch you can learn for handsewing. All of the videos on the Sewn Company Tutorials playlist are good instructions.

V. Birchwood also has a great playlist full of videos on historical sewing. (Her other videos are worth watching too, especially this video on sewing as active meditation.)

How to Sew a Simple Strong Seam by Hand: Speaking of historical costumers, Bernadette Banner is a joy to watch. Her book Make, Sew and Mend is one I recommend if you prefer learning from books.

And speaking of sewing as meditation, I'm a huge fan of "slow stitching", which is essentially using the process of sewing and embroidery as a creative, meditative act without necessarily worrying about producing something specific at the end. I love doing freehand embroidery and random designs when I'm in that mood. If this sounds interesting, you can check out Daniela Mellen's Learning to Slow Stitch playlist.

Specific Skills

What I Learned in 1 Year of Hand Sewing: This is the video that taught me how to use a thimble after I'd been sewing for thirty plus years.

How to Alter Clothes for a Custom Fit!: Being able to do small alterations has been an absolute godsend for me, as a trans man who wants to wear masculine clothes but has Those Freaking Hips.

The Ultimate Guide to Hand Sewing Buttonholes and Sewing a Zipper by Hand both do what it says on the tin and are useful references to keep handy.

How Victorians Mended Their Clothes: A Lesson in Darning: Visible mending is very popular now, and I love it, but it's also good to know the techniques for less visible mending.

Tips to Help You to Hand Sew Faster: This isn't so much the opposite of Slow Stitching so much as it's about efficiency and good technique.