What is the machine called that you weave on?
A loom, and the person operating the loom and doing the weaving is called a weaver.
Which is the warp and which is the weft?
Most often the warp runs vertically; think of these threads as the ones that form the structure into which the weft yarn is then added horizontally.
What loom should I buy?
All looms have their own unique purpose, from a cardboard loom, to peg looms, to table and floor looms. The best loom to use will be different for everyone depending on your hopes and ambitions, previous experience and space available!