This is a very important question for SEO. I bought a used domain without realising that there were a lot of inbound spam links. This could at worst cause a penalty from Google, at best it was a bit embarrassing as I then appeared to be the spammer.
OTOH buying a used domain with some existing good inbound links can be useful, likely to be very expensive though.
Redirecting domain to domain should not harm you, at one stage Matt Cutts of Google did say that a 301 can lose a very very tiny amount of page rank.
However once Google picks up the new domain it's no longer using the redirect which would then only be relevant for other static inbound links.
If you make a list of your existing good inbound links, you can contact the owners of the sites and ask them to update.