Lots of people are confused when it comes to which materials and tools to get, and that's understandable! There are so many different things out there made for working with clay, and even though they're all cool in each their way you far from need all of them to get started.. you don't even need all of them when you're and expert. I've tried deviding materials into 2 categories. the first one is the tools I believe are necessary, the second are the materials and tools you can get if you want, if you feel you need some of them or whatever reason :)
The things I believe are necessary...
*Clay - of course,.. you need some clay, but you don't need all colors and shades available. Start off with the colors you think you're going to need the most, or buy the primary colors; white, black, red, yellow and blue.. The clays I use the most are; White, fleshtone, caramel and chocolate brown. the brown shades could have something to do with my obsession for chocolate ;)
*Roller - it doesn't need to be anything fanzy, but you need something to roll out the clay. unless of course you're never going to make any flat surfaces with a uniform thickness. For a long time I used a small plastic roller from a playdough set, I later switched to a larger white plastic pipe (made for the drain on a sink or shower I think). Finally I switched to a pasta machine, but more on that later.
*Needle tool, and perhaps something with a more rounded side. my favorite (and almost only tool for a long time) was a "meat-pin". it had the needle shape at one end, and a loop on the other. the loop end iss perfect for creating texture, smoothing things out and lots of other things. it's still my most used tool.
*Work surface - you need a proper work surface. something smooth, something that's easy to clean, and something you can mess up without worrying about it. Lots of people use a white floor tile, others, like me, use a glass plate. The one I have is made to hold candlelights, just a flat round piece of glass.
*Blade/knife - an absolute necessity is a sharp blade or knife. whether it's a craft knife or a blade made for polymer clay is up to you. I use craft knives with adjustable blades, super cheap ones bought in a local discount store. but I also have the actual polymer clay blades. I love both. the blades are the sharpest and work best for most things. but I like the craft knife for "detail cutting" - cutting out shapes etc.
The things you don't absolutely need... but those that are still nice to have :)
*Cookie cutters - a great help for making precise shapes and for use when making more of the same item.
*Chalk pastels - I was really close to putting this on the list of things needed. of course you can do without them, but they are awesome for getting a realistic look when making miniature food. To me they're an absolute MUST. so consider them needed or extra, it's up to you :) if you do decide to get some look for 'soft pastels' and you'll also need a brush to apply them. the brushes I used are mostly the ones sold with kid's watercolor sets.
*Liquid clay - Translucent liquid clay is a really cool addition to your list of materials. you can use it for making whipped cream, icing, sauce and many other things.
*Corn starch - if you decide to make molds I suggest you get some corn starch to keep the clay for sticking to the mold.
*Glaze - not a necessity, and for miniature you don't have to glaze everything, not all food is shiny. but it does add an ireplacable effect to some items. if you're making charms it also helps to protecting them.
*Pasta machine - I believe that this is something you can definitely live without! I didn't buy it right away, in fact it's one of the newest additions to my collection of tools. it's a really great help if you're making lots of the same thing, if you need a uniform thickness or if you're making canes. it really does make a lot of the work easier.
*Sculpting tools - you can get lots of tools made for clay sculpting. I didn't buy these until I started doing figure sculpting. you can do without them, but again, it's just one of those things that makes the job easier :) the tools I have were sold as 'dental tools' and 'cake decorating tools'.
*Craft sand - white craft sand can be used for sugar, salt and texture in general. a lot of fun to play around with. it especially was an amazing thing to have when I focused on charm making. I don't use it just as much for my clay miniatures, but it's still nice to have.