Which version of MakeHuman should I use?

There are in practice two relevant current versions of the MakeHuman standalone GUI application: 1.2.0 and 1.3.0. Functionally, there isn’t much difference between these two. The main visible difference is that 1.3.0 contains bodyshapes, which 1.2.0 does not.

In 1.3.0, attempts have been made to solve some of the most common graphics problems (see what is the current status of MakeHuman for background). While this has solved problems for a large subset of systems, it has also introduced other problems for another smaller subset of systems.

In summary, your best bet is to install version 1.3.0. However, if that does not start on your computer, you could also give 1.2.0 a try to see if that works better.