Alot of people will suggest Blender since its free.
I tried it about 8 years ago and hated it, I gave it another chance last year and was still frustrated beyond belief.
Lots of people swear by it and I've seen beautiful projects come out of it so don't ignore it completely.
Lightwave is pretty safe for beginners but I haven't touched it in years so I cant say much more about it.
I've been using Maya for 5 years now. Its free if you are smart enough.
Its got everything though. Not the easiest to start out in without some help.
It really depends how much time you want to put into it.
A few youtube videos and forum posts should at least get you started.
Unless you are going to take a class on it, its just a bunch of trial and error.