I DEFINETLY HIGHLY recommend Blender. It is free, and no, it is not "shareware"/"demo", it is completely free, as in: Take it or leave it.
www.blender.org
It is just as advanced and can do exactly the same stuff as the commercial applications, mainly Maya and 3DS Max used in industries.
Blender is becoming increasingly popular in the computer graphics industry too, but mainly in some parts of the U.S., Netherlands and Germany.
If you have never tried 3D modelling/animation before, I highly suggest you try Blender, even though it has a steep learning curve. It only gets worse if you try out the commercial
software before you learn Blender, because then you get used to, lets say 3DS Max and you expect Blender to behave that way. It doesn't.
Start with Blender, there are plenty of tutorials to get you started, and I can recommend Andrew Price's tutorials about Blender,
his website and tutorials are located at:
www.blenderguru.com
There is also www.Blendercookie.com with lots of other high quality tutorials.
Blender is free, it may be used for both non-commercial AND commercial purposes, it is Open Source (meaning everyone can edit the source code if they know how to do it), and it has sophisticated material editing, compositing etc. In short, it has everything you need and want, and even more.
Don't EVER pay for 3D modelling software. It is a waste of money, when you have Blender.
Blender works well with GIMP (again... that's like Photoshop, just free/Open Source). Most Blender users prefer GIMP instead of Photoshop, so I suggest you download GIMP too.
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Some good advice:
* When you open Blender, set it to Cycles rendering (the tutorials will show you how).
Only, ONLY use Blender tutorials where they are using Cycles (unless you are only modelling, and not applying textures/materials to your objects), it makes life easier. It has both GPU and CPU rendering, Blenders' Internal renderer is obsolete/outdated, don't ever use it.
* If you go for GPU rendering, which is faster, I suggest you get an nVidia card. Blender currently only supports nVidia, unless you are using CPU rendering.
If you want to spend money on a new computer, I highly recommend an Nvidia graphics card with AT LEAST 4 GB memory. Preferably nVidias Titan graphics card works pretty well with Cycles rendering.
* Buy an extra monitor. Just a cheap one. 3D modelling and just about all other graphics software works best on multiple monitors. You can use a single monitor, but you need a big one. I prefer a big monitor as my main monitor, and a small one as my secondary. It gives that extra space you need to focus on your graphics work. It also makes it possible to watch tutorials on one monitor while doing it yourself on your main monitor.