I wouldnt use windows movie maker even for video editing.
What kind of thing are you thinking of 2d or 3d or animating video effects? And what kind of animation humans animals or just moving objects about?
If your wanting to get into animation the best thing you can do is buy the book - The animator survival kit by richard williams.
You can buy a computer arts magazine which will probably give you some trials or free software on coverdiscs.
Blender 3d is free and a open source program i've never used it so I cant say how good it is.
Ones to buy (but they also have trial versions)
2d is easier, good programs for that are Flash (but thats mainly used for the web)
Toon boom is pretty good thats used for 2d tv shows etc
Theres anime studio which uses a 2d bone structure which sounds very good never used it myself but that sounds quick to animate.
3d is alot harder but you get more impressive results and you can do 2d animation in it (south park is made in Maya a 3d package).
There is alot of debate about which 3d package is the easiest they are all about the same you still have to put the hours in but I would say SOFTIMAGE XSI is the easiest I have tried once you get round the principles of it.
MAYA is the biggest industry package I would say but i found XSI to be a bit more forgiving.
3DStudio Max is the most popular for smaller companies and enthusiasts and you'll get the most tutorials and help on the web.
Postproduction packages, adding effects to video which can be animated also green screen removal etc.
Adobe after effects is the biggest enthusiast software so lots of books and tutorials. Combustion is pretty good to but I'd say After effects is more suited to beginners.
Shake is what they use on most feature films but it only works on macs now.
There is also a program called Animation Master by HASH, a websearch should get you to their site. It might have less of a learning curve than Maya or the other expensive 3d programs.
Heard good things about that package, havnt checked how cheap it is XSI has got a basic package thats pretty cheap (for a high end 3d package) with cut down features that your only gonna miss if your seriously into animation.
I would maybe not use flash as its mainly for web based and quite pricey anime studios only £30 ish for the basic and £150 ish for the advanced i'm really tempted myself actually because the bone system sounds really quick and easy to animate.