How to modify 3D models for 3D printing?

I would recommend (http://www.meshmixer.com/) to do al necessary editing before 3D printing.
It is powerful jet very easy to use software and gives you print volume reference and basically every other tools you need to prepare models for 3D printing (things like analyze mesh and automatic support material functions and lots of other editing tools).

For example if you want to rotate the wheels of some model car, you could cut them off rotate and glue them back on and paint away possible irregularities using the paint/sculpt tools (if model was single mesh).

Regarding the other 3D models you would want to print (but not jet setup to do so), you can basically get them into Meshmixer (if you have OBJ or STL file of the 3D model)and make them watertight using the merge/remeshing functions and use paint/sculpt tools to clean things up and make everything into one nice watertight 3D printable mesh.

3D Coat voxel sculpting tools are also recommendable for making single watertight 3D printable meshes from 3D files that contain many parts. I experience it as fastest way to get to watertight meshes but it is a bit harder to grasp the concepts of voxel sculpting for a beginner (in particular the scale and density settings). 3D Coat also has tools to pose a character so that would be something for you but it lacks other tools present in Meshmixer. For that reason I use 3D coat as well as Meshmixer in tandem when doing something for 3D printing.

Generally Meshmixer will cut it and is capable of doing most things you ask and is good way to start, it can do lots of things, and crazy part, it's completely free.

Ps. if you don't want to get into 3D editing yourself, you can also just ask the publisher of the 3D model to make the necessary edits you would like to have (that will probably cost some extra).

CGtrader has build in communication system to make direct contact with the 3D designers (that's best part here).

If you click the nickname above any item you find here, you will enter that given designers profile and find a contact button in top left corner.

Most will be eager to help you out and if they don't you can for example post your requests as a job offer here (https://www.cgtrader.com/jobs), (make shure original author is ok with that).

Job offers appear in the dashboard of all designers so it is very likely you get to someone hoe would like to help you out.

Hi,

Thanks so much for your answer. I'm still WAY too new at this to attempt anything on my own so I think that I'll try contacting individual designers first. It'll be some time before I'm familiar enough with the processes to tackle anything on my own. Still, I love the things that I see here and hopefully some of the great artists whose work I see would be willing to work their designs a bit for me provided that I pay.
Your answer was very detailed and will help guide me into the process of learning to do these things myself. I really, really appreciate that! I now know that it is possible and have an idea how to go about it.

Thank you!