Mitsu
Fleece or felt are pretty good fabrics to use. There are quite a few plushie tutorials here: ^_^

Neko
(I'm answering as if you're a novice to sewing, disregard most of my answer if you're familiar with a sewing machine, please =^.^=) As the above poster stated, fleece or felt are good fabrics to use; this is because they don't fray at the edges if you don't bind them. They also are more resistant to the fibers you stuff your creatures with sticking out. Sometimes (I think it happens when you have a low thread count in your fabric) the fluff inside whatever you make starts to come out as itchy hairs. Satin is particularly horrible about this problem. I'd suggest using a sewing machine if you have access to one, it makes much easier. Another suggestion, and the best I have, is not to start too small. You may think that it'll be easier for you if you begin with a small plush because if you screw up they'll be less material waste, or less margin for error, but trust me - the smaller something is, the harder it is to sew. Begin with more simple shapes, and then expand to harder things. You can also get great advice on exactly what fabric you're using if you ask the nice ladies (and sometimes men) in your local fabric store. Tell them you're making a stuffed toy, instead of an anime doll if you're afraid of getting looks. (In my town, if you say "cosplay" or "anime" you'll get a negative reaction. You can also find patterns for sale from pattern books and with a little editing, they could turn into a character - maybe a teddy bear could be stylized to Ranma 1/2? Patterns come with instruction sheets telling you how to put the pieces you cut out together, and starting with a pattern you don't have to worry about all the parts matching up as much as if you just designed it yourself. You may also find a book about making stuffed animals which could come in useful as it should depict different techniques for creating plushies that you can take and apply to different projects. Best of luck on your journey into the wonderful world of textile crafts!