Does modern Blender still support .obj files? I use ancient Blender (2.68) and it does. Although, it might not be the best choice for every task. One issue (that I know of) is when meshing objects with joints, info about the bounding mesh doesn't get processed correctly or something.
Most 3D programs support obj, and I think most versions of Blender does. You may have to download plugins, though I have a feeling Obj is supported by default since it's a very commonly used format.
When it comes to meshing with skeletons, I'm not so sure. The plugins I've so far found have been for older versions of Blender. It's possible you can use the SMD file format if you get the right plugins.
I'm almost sure you can export as SMD from SimPE, but I haven't tried it. You probably have to select the file type manually. You may need SMD plugins, though. I think I had to download those manually.
Just so you know, Blender does have a very steep learning curve, particularly if you've used various other meshing programs and are very familiar with the outlays. The tools are placed very differently compared to most other meshing programs, and it's not intuitive at all. Be prepared to read a lot of tutorials on the basics.
I think I've got either 2.70 or 2.72 of Blender (been a while since I installed), and whatever version it is, it does support Obj files. I don't think it's the newest version (pretty sure it's up to 2.8-something by now), because I had to have one compatible with Sims4Studio. Nearly all meshing programs I've worked with have had OBJ support (occasionally via extra plugins), possibly because it's one of the simplest and most versatile mesh formats.