Best way to avoid duplicate contents punishment from google when doing redirects

How do I phase out an old blog with a new one? I have some posts on my old site that I wish to transfer to my new blog site. However I’m afraid that the search engines will punish me for “duplicate content”.

I figured a solution to the problem would be to do a 301 redirect from my old post articles to the new ones. Is this the proper method? Will it stop the indexing of the old posts and not consider the new post content as duplicate?

When I set up the 301 redirects on Hostgator they only work until I add another one. I have to keep deleting them all and redoing them all. Very frustrating and 2 calls to tech support resulted in that same solution? They said that it may be the “htaccess” file. They also said to maybe try using “url redirects” instead of “301 redirects”. Any thoughts?