Canvases and Paper
As a beginner, it's difficult to decide how much to spend on your painting surface. On the one hand, your painting is only as durable as what it's painted on, and it makes sense to spend a little more money on ensuring your time and effort aren't wasted on poor quality paper. On the other hand, you might feel more free to experiment if you're not worried about wasting expensive paper or canvas. It's up to you.
I do feel that it's most important to invest in good paints and brushes, so most of your money should go towards these. At the beginning, buy small quantities of student quality canvas or paper, and as you improve, work your way up to better quality.
Acrylic Paintings
Most acrylic artists eventually graduate to stretched canvas. However, stretched canvas is more expensive and you might want to try some other options for your first few paintings. You can use stiff paper or wood panels, but I would recommend starting on canvas board, which is primed canvas stretched over stiff paperboard. Canvas board is much less expensive and more durable than stretched canvas, but still gives you the canvas texture that looks so professional. You can hang it on the wall nicely without a frame too. I would recommend starting in the 9" x 12" size for your first painting, and working your way up. A 9" x 12" canvas board costs about $1, and you can paint over it once or twice with plain white paint and start over if you want to.
Watercolor Paintings
For watercolor, you'll be buying watercolor paper. Cheap watercolor paper is just regular thick paper with texture, expensive watercolor paper is made of cotton, and moderately priced types contain a mixture of the two. Don't use sketch paper or other thin papers, since they will warp and get soaked with water.
There are two kinds of watercolor paper: hot press and cold press. This is jargon that refers to the manufacturing process - all you need to know at the beginning is that hot press=smooth, cold press=bumpy. Whichever paper texture you choose is up to you. I prefer cold press because I like the bumpy texture.
The other consideration in paper is thickness. Thicker paper will buckle less, but costs more. I would recommend at least 90lb ("pounds" refers to the density), 140lb. is standard.
You can buy watercolor paper in a pad, a block or single sheets. A block is like a pad but is sealed on all sides, to keep the paper rigid and keep it from buckling while you paint. The block is very useful if you're planning to travel with your watercolors but it costs a little more. At art stores, you can buy single large sheets of watercolor paper. This is a great deal, because you can cut the sheets into whatever size you like, and it gives you an opportunity to try different thicknesses and textures without having to buy a whole pad. Don't forget, if your painting doesn't work out on one side of the paper, you can let it dry and use the other side for practice.
Get a plastic document folder for your watercolor pad. They're about $1, and they'll save you a lot of grief by protecting your pad from spills, smudges and crumpling in a backpack.