I don't know a huge amount about adsense so i cant give you much in the way of advice on that front. All I will say is, old domains are worth a lot in
SEO terms so you would be wise to try everything you can before redirecting.
301s are great! From my experience they work perfectly and as long as they're in place all the old links will pass the link juice and ranking factors to your new site. One factor to check is that the site you are redirecting to has the same type and amounts of content as the previous site. So make sure all title tags, body text etc is up to the same standard as the previous site or you may end up loosing positions.