As Ar said it would depend on what you want to do and expect to get back out. If you have a lapidary club locally, it would be worth trying to pop in and get an idea of what equipment is used.
Depending on what size stone you want to cut will depend on what size saw you will need, but if you have smaller stone you may not even need to cut them.
The most basic way to start polishing rocks is with a tumbler. You can get these in different sizes (or make them) depending on size of rocks wanting to be polished.
For cabbing it is easier to use a wet grinder or sander with diamond wheels, though for the early rough grinds silicon carbide wheels will get you by, but they must be wet grinders. I did start doing a bit of cabbing on a flat lap (spinning diamond disk with water dropped on it) but had some issues with flat spots and grinding my fingers down. Buying new lapidary grinders are not cheap, but good bargins can be found if you are persistant and patient.
You can do some basic cabbing with just wet and dry sand paper, but it is a tedious and slow process.
A dremel can also be used to carve/shape and polish rocks, but again you will need an assortment of bits in varying grits.
Faceting seems to be one of the more expensive parts of cutting (from my point of view) whilst cheap machines can be found, you cant expect great results and new machines come in from about 3k upwards.