Buying and benefiting

Having bought a domain, how do I benefit from its listing?

[bluegrass]

I have a site that is well listed in Google.

I have bought the domain of another (competitor) site, that is also well listed in Google.

I want to use the new domain to point to my existing site. What is the best way to do that AND (if possible) inherit the Google listing of the new domain?

Does just pointing the domain name to my home page do it? Does pointing to a Redirecting page lose it?

Thanks