Question about redirections???

I had a website running and the domain expired and I did not renew. Someone else bought it and started running advertising on the domain.

I then made a new site on a new domain but a similar topic. I used some of the info from the old domain and am ranking ok it has only been a couple of months.

The old domain expired again and became available so i purchased it one year on. The old domain is still getting very good traffic and has the advantage of being much older. A few backlinks and new articles and im sure i can get back on to page 1 of google again.

I was thinking of just setting a redirect from the new domain to the old one and joining up all the information from the new site with the old one.

I wanted to know whether google and SERPs will penalise me in any way?? Or is my plan a good one. I know some will suggest to have both sites running parallel but I really want to just concentrate on one site.

I also heard somewhere that backlinks to a redirect are not considered as good links?? not sure if this is true.

Both sites are on the same hosting by the way in case this is also an issue.

Any advice on the above would be appreciated.