Round, square, and rectangular tubing is what is generally used in go kart construction. Round tubing has a bit cleaner look, tends to be a bit more of a pain to build with and usually requires a tube bender. Pipe benders do work okay bending tubing, however with tubing be measured by outside diameter, whereas pipe is measured by inside diameter, pipe dies don't always fit the greatest for tubing.
1" tubing with .125" (1/8th") thickness is a good start. A rule is, a larger diameter with a thinner thickness is usually stronger than a similar size diameter with thicker walls, plus you can sometimes save on weight. Keeping weight to a minimum is paramount with go karts. Mild steel is probably the best metal to build a go kart out of. Chromoly (Chrome Moly) is a pain to work with, as it usually needs to be pre heated and post heated to be welded as to prevent cracking of the base metal and filler.
Other metals (aluminum) can be used, however, you need to be well versed with working with the stuff.