In the game, I loaded up a new world and got a sparse supply of sheep and spiders.
Make a sheep farm. Basically get some sheep (at least 2) in an enclosure - simplest is a two block deep area that they can't jump out of (Place a ladder one block off the floor for yourself to get out) - and feed them wheat every 5 minutes to breed up a large population. Then you can shear them for wool.
Tip: if you want a specific color of wool, dye the sheep that color and their wool will always regrow in that color till you dye them another color.
Your best bet is to explore around. Spiders are pretty common in underground areas, especially if you can find an abandoned mine you can harvest the webs (with a sword in hand). They will also spawn at night (unless you are playing peaceful). You may even find a dungeon in your underground travels that spawns spiders. You can turn this into a slaughterhouse and farm away.
As for finding sheep. they commonly appear in meadow biomes so wander around to find them and then lure a few back (hopefully you don't have to travel too far from your home) and create a little fenced in area for them and start breeding them.