Install 1.5.5a on different server, use database from current v1.5.0 site

I really wanted to upgrade my 1.5.0 because I have Ceon Advanced Shipper and Apsona Shop Admin (which, BOTH of those apparently can't be 'had' anymore), along with some other customizations that I need, but after considering the amount of changes that have happened over the last few years, including Security and Responsive issues, I have decided to build a brand new site. I'm going to put new zencart build (same domain name) on a different server (same Godaddy Hosting, I just have another GoDaddy hosting account I want to move the site to). I have many products, so I need to use my current database and photos. What, exactly do I need to do? Any links to existing articles, and/or advice here would be greatly appreciated. Thanks!!!!!!

1. While you can temporarily use a copy of the "current" database, when it comes time to actually "go live", if you want to preserve all the transactions that happen between now and then, you'll need to re-import it to the other server and upgrade it again, and then reconfigure any new settings in your admin and re-run any plugin installers that make database changes.
   So, take very detailed notes of all the things you do so you can quickly re-do them again when it's time to go live.

That said, then this comes into play:
2. http://www.zen-cart.com/entry.php?3-How-do-I-rebuild-my-site-on-the-new-version-instead-of-upgrading ... you're just doing it on a new server, and instead of the "go live" applying to the original database, you've said you're doing it on a different server, so first you put the old site down-for-maintenance, copy the db over, do the upgrade, etc as in the paragraph above and in the link above.
I'm repeating myself now.

3. I recommend a "practice" of your "go-live" activities where you go through all the steps above but WITHOUT pointing the domain to the new server until you're satisfied you know what you're doing. ie: you may do multiple transfers of the database and re-upgrade and re-configure things, until you're sure you've got it clean.

But really, this isn't much different than just leaving it all on the original server ... except that the new server could potentially be running newer more modern server-software, which would be a good thing in the end.