UltiSnips requires py >= 2.6 or any py3

You don't provide much information to help. You can check whether your Vim has Python via :py print "yes". For the Python version, check the :version output. It will contain something like -lpython2.7.

When you compile Vim yourself, you need to enable the Python integration by passing ./configure --enable-pythoninterp.

I had the same problem with NeoVim on Ubuntu. Running :CheckHealth pointed me into the right direction. Creating the following softlink solved the problem for me:

sudo ln -s /usr/bin/python /usr/local/bin/python

Download the source code from http://www.vim.org/. Then

1. cd vim
2. make clean
3. ./configure --prefix=/opt/local --with-features=huge --enable-pythoninterp=yes --enable-multibyte --with-vim-name=vim --with-python-config-dir=/usr/lib/python2.7/config-x86_64-linux-gnu
4. make
5. sudo make install