Re: first fly tied
Congrats! It's a great way to start!
I do wonder if you need to get some newer materials and thread. If the thread was 3/0 you'd have to be putting some good pressure on it to snap it a bunch, on a size 10 hook I'd use 6/0 or 8/0. 3/0 shouldn't snap too easily so I wonder if it's gotten weak over the 30 years or if something in your bobbin tube is cutting it. If you can, pick up a bobbin with a ceramic tube - the ones I get are only like $14 or so and buy a couple new spools of tying thread.
Just pick a couple patterns you want to tie, make a materials list, and go to a fly shop and get what you need. I'm sure you've read wooly buggers are a great place to start. Oh, and ask a lot of questions and post a lot of pictures!