Need to know a few things

Consider the width, most oftern used is 24" vinyl's or smaller widths heat applied vinyls. The more expensive cutters come with multiple software. You can purchase a good cutter from $500 to $1500.00.

Well vinyl cutters come with array of options:
Speed/accuracy/width/optional registration mark finders ect...
You can buy a descent one prob. in 1200 dollars rand like a Roland
You will also need rolls of vinyl which is pretty cheep
Masking tape and applicator
"software" now if you can Adobe Ai than you can get a plug in called Cocut for like a few hundred bucks
Flexi sign has one for 500 bucks but Roland cutters usually come with there own software
Squegee is needed (60 cents)
so in end you looking at around oh 1800 dollars range but Sign Supply & T-Shirt Supply for Vinyl Cutters & Inkjet Printers - Beacon Graphics, LLC run starter kits that will have everything you need I believe ... I would call them and ask about it
those are just some stuff for starters but as you progress you will see you need little odds and ends during your journey like application fluid, tweezers ect.

How does the cutter work? How do you do multiple colors? How and what kinds of signs can be made?

Ok don't know how old school you are but if you remember the old plotter architects used with a pen holder?
Well instead of a pen being used, it uses a little knife thingy and that scores vinyl and you peel the waste off
Multi. colors is achieved with softwars in color layers umm go to youtube and type in vinyl cutting and might help you understand alot better in that point of view

Different colors are layered just like in screen printing, cut one color (print) then the next, and so on, but try to keep it simple, or weeding becomes a nightmare.

I'd recommend taking a look at the Graphtec 5000-40 (Craft Robo Pro) if you will just be doing smaller things. Its built the same as the more expensive models, but is only $899 at USCutter. It doesn't come with a stand, but I wish I had started with it because even if I out grew it because of needing bigger media, it would still be a solid backup cutter.