301 Redirect for a Website with Potential Penalty

I have a website which has been running for around a year, was slowly trying to build links to it and it was working until early June when it seems to have got hit by a Penguin penalty. I've tried to recover it but without much luck.
My next step is to transfer all the content over to a new domain and shut the old domain down. What is the best way of redirecting the old site to the new site in the short term so I get the traffic it's still getting, whilst I try and build links up to the new domain. Also, will this cause the penalty to transfer to the new domain?
I'm sure there is a way of doing this properly, as I've seen other websites do it.
Any help appreciated.

A 301 redirect will pass much of the link juice but will also pass a penalty, don't know about 302.. waiting for another reply

The penalty will transition to the new domain. The best way to redirect the site is a 301 redirect.