Which way is better to change my domain name so it doesn't affect my search engine rankings?


I've searched this group, but haven't found an answer for exactly what
I'm trying to figure out.

I have a website for my home business, that is ranked between #2 and #7
on Yahoo's 1st page (depending on if you enter the singular or plural
version of the keyword phrase), Altavista, and MSN....but these
rankings are mainly for one keyword phrase. I've been reading a lot
about Search Engine Optimization, and decided to overhall my website.
I decided to change my domain name, including keywords in it, to help
even more with my search engine rankings. I don't want to forward my
new domain to my website, I want it to be the actual domain for my
website, and forward the old domain to it.

I called my hosting company (godaddy), to see if they could just change
the domain name, and they said they couldn't, that I'd have to set up a
new hosting account, and delete the old one.

Ok....so which way would be best so that I don't hurt my search engine
rankings on Yahoo, Altavista and MSN? Should I leave my old website
and old domain in place for a couple months until I see my new site and
new domain name hign in the rankings? (will having two almost identical
sites hurt me or get me blacklisted from these search engines)
Or....should I just point my old domain name, to my new site? Would
the search engine bots follow the link from my old domain to my new
site, and then update the search engine listing? Am I just going to
end up having to start from scratch with my search engine rankings?
OR....should I just leave well enough alone and keep my old domain name
and just work on editing my original website?

Google illudes me. My site is no where to be found in Google, although
Google does know about it... only 1/10 ranking though. Is the ONLY way
to get listed in Google through links? I have a different website
that has excellent placing in almost every search engine, and it is
listed in DMOZ, but couldn't get that one into Google either....until
I placed a paid listing on a popular website which has a google rating
of 6/10, and THAT listing of mine shows up high in Google....but not my
own site that is linked from my listing.

SEO sure is a Science!!!

Thanks so much!