how do I get most of my standard linux utilities and commands on Android 3.1? by standard, i mean just what users often get by default with one of the popular distros.

for example, uname, finger, vim, tmux, etc.

I have a galaxy tab 10.1 (android version 3.1, already rooted)

Also, I read somewhere about setting up a chroot on android to run full-fledged linux distros, such as debian. Is that possible?
BusyBox for rooted devices gives many of Linux's standard utilities.

In terms of a real Linux distro, there are tons of How-Tos found on the web with a simple Google search.  Specifically, here is a step-by-step guide from XDA-Developers forum on building a Debian image for, and installing it on, the Galaxy Tab 10.1 tablet.