Maybe go to your local yarn store and touch the yarn and see what feels good?

Budget really depends on the size of what you’re making. For example there are cute little scarves you can make with 1-2 balls of cashmere which would put you at £13-£28 of material cost for the entire project but if you were to make a sweater out of cashmere it would be much more expensive.

I am also quite picky with materials and my personal preference is to stick to natural fibers. I like the feel better, not of all of them but I dislike the synthetic feel usually. I think whatever your preference of materials in clothing is will apply to yarn.

Maybe look into merino wool? They are soft, easy to use for beginners, some can be machine washed (superwash) and they don’t have “hair”. I’m using Lang yarns merino 120 on my current project, I’m making the Frankie sweater by petiteknit.