"Is IronPython mature enough for these purposes yet?"
The snarky answer is "obviously", since it's a first-class part of visual studio.
http://search.microsoft.com/results.aspx?mkt=en-us&setlang=en-us&q=ironpython
A better answer is "yes". It really works, has really worked for years, and is compatible with other Python run-times that have worked for many, many years.
Here are the instructions: http://www.microsoft.com/downloads/details.aspx?FamilyId=55932211-0D7E-4C6E-9B18-8F9D2AC1EE43&displaylang=en
"Would it be better to forgo IronPython while learning, and stick to the official version 3 distribution?"
This doesn't make much sense.
You're working in .Net, so IronPython is your best choice. The "forgo IronPython" is hard to parse -- are you thinking of using CPython? It works, also. And works well, but it might not work well with your other visual studio tools.
"stick to the official version 3 distribution" makes no sense at all. There are two parallel distributions, both official. There's 2.6 and 3.x. They will both exist in parallel for the foreseeable future.
You should start with whatever version works with the tools you want to use. At the present time, your tools probably work better with 2.6 than 3.x. At some point, you'll notice that your tools are migrating to 3.x. Then -- and only then -- you can migrate to 3.x.