Hi DVDStar and welcome to WPW.
A 301 redirect will tell search engines it is a permanent redirect. It's the preferred redirect method, while other types can actually get your site in 'trouble' (even a ban from Google, in some cases).
You can set it up in a .htaccess file in the root directory of your site.
All benefits coming from the old domain will be passed to the new domain, generally speaking, in theory.
There are exceptions, but over time that should be the effect.