Ray Trace

Hаppy бirтhдаy то...wаiт...iт's noт мy бirтhдаy?
The ones I use and recommend are Blender, Maya, and 3DS Max.

Maya is the industry standard but it costs money. You can get a free trial version as a student though. 3DS Max is similar, also by Autodesk, and that's the one I use for general purpose modeling like rigging and rendering and fixing UVs and what not, but Maya can do all of those too just differently. Blender is the open source model program but imo has the least friendly UI out of either of them. Blender also comes with a video editor too.

Google Sketchup is another one but it's the one I have the least experience in so not sure how much its functionality is.

Sailor Mario

Mushroom Kingdom's most out-there sailor
The free trial by Maya, student version, works like a full version and its license doesn't expire for 2-3 years. You should be good getting that version, as new versions come out every year, so you can just download the new year once your old Maya license expires. It's really neat, and I didn't have to pirate it.

You should first get familiar with the interface with these programs, and I recommend you look up models from models resource. From there, you can have a nice look at some official models, stored in .zip. in the program. Maya and 3DS Max should be able to read .fbx files while all programs should open .obj. Blender probably can open .fbx or it requires a plugin. .dae files also require a plugin. There are big differences between obj and fbx by the way, and there are some differences between .fbx and .dae. If you like to pose models, then I recommend opening the fbx or dae ones.

You might run into materials issues, such as models appearing all white, due to the texture links within the model pointing to a different location (like C:\\Mario's Uploads\Models\Notyourcomputer\), so depending on the program, my sister and I can help you set up the materials. I don't know which program you'll settle right now but you should try Blender, which is free, though I can't help you with it because I'm not familiar with its interface at all, or Maya, which needs you to sign-in and get some student licenses that last a while, but I can certainly help because I've used it a lot.