Cutters
This includes scissors, blades and everything else that cuts. You can cut pclay with specialized tools that can be bought as a set but the cheapest way is to have a small cutter. Small cutters are better than big cutters because they have a thinner blade. Personally, I like smaller more delicate cutters because they are easier to handle. When it comes to scissors, anything will do but if you work with paper you will probably need some specialized tools. With pclay I rarely use scissors.
Toothpicks
Yes, this is funny but it's actually my favorite tool. I can make small holes and I can also apply small quantities of material on other materials. You will definitely need a toothpick or something similar when you are working with Fimo or other types of pclay. Especially if you do small figurines or stuff like that.
Then you have these
When I started playing with pclay I made some of them from pclay itself. Although I don't think you need them all(unless you sculpt) having some of them is very handy. Unfortunately, most good sets cost pretty much for somebody who just started using pclay so I only recommend them to those who are taking this serious. Also, make sure that you need them and since there are many sets available at different prices, check more stores, compare prices, compare quality, etc.
Pasta machine
You will want this if you are aiming for perfect canes and usually for perfect designs. I don't use a pasta machine for my girlies but it's very handy so buy one. A tip here would be to actually buy a pasta machine than one that is designed for polymer clay because pasta machines are cheaper and more durable. (at least they seem so). If you don't have a pasta machine you can get a roller. If you can't get or don't want to get a roller you can use a glass bottle. :)) it's pretty handy until you get the pasta machine :))) or a roller.
