Hi, I'm also using hostgator to host a django project.
first of all note that they have different plans with different features, what I'm going to write applies to their shared hosting plans.
Looks like they are using some version of centos, which comes with python 2.6 I believe.
Installing a python from source on your home folder is a good idea, but unfortunately hostgator blocks access to gcc.
on the other hand they already have python 2.7.3 installed, juts use python2.7 as the executable, try running "python2.7 -V"
btw, they also have python2.6 for 2.6.6 and python3 for 3.2.3
after that you should use virtualenv to create a project specific env so you can install things using pip. download the virtualenv.py file to you project folder and run it from there. for the index.fcgi file you should put this in the first line:
#!/home/username/projectname/env/bin/python
other than that I think it should be standard, maybe I should do a blog posting documenting this better. let us now if this works