Lace weight is rather thin, cobweb weight is about the thinnest wool you can get (that refers to how thick the wool is). Laceweight is generally considered a 2-ply.
Worsted is another (heavier) weight wool i.e. it is thicker.
For lace, you want a fibre that is all or mostly animal fibre. Wool, cashmere, alpaca, silk, mohair, etc. These fibres block and that shows the pattern later. Synthetic fibres will stay crinkled up, they will never open up and show the beautiful pattern. I would say at least 75% animal fibre, wool is a common favourite.
There are lots of tips and tutorials and explanations online about doing lace, it takes a while to get used to but is very rewarding! You can also search this forum to see previous discussions about a topic, so you might like to search 'lace'.
Eunny Jang's blog has some good but quite technical explanations about lace knitting.
Welcome to KH!