Hi,
For all of the websites I run whether it be CSK based or not, I do all of my developing on a local copy of the website and then upload it once I'm happy with the changes. The main benefit here is visitors won't have the chance of seeing half-finished updates while you're in the processof making changes but it also means that it's quicker to do as I find using Visual Studio against a local website is hugely quicker than working remotely.
Depending how you published your site to UltimaHosts, the easiest way to get setup locally would be to copy the content back down to a new website in VS. Obviously if you published the website in a pre-compiled state there would be no source code to redownload so you'd need to either start with the original files you uploaded in the first place, or a fresh copy of the CSK.
As for the database side, I keep the local connection string the same as the live one so that while working locally I'm still targetting the live SQL database. This means you don't have to duplicate changes in a local SQL DB up to the live SQL DB but you do have to watch out for gotchas if you make changes to your source code and SQL objects as the live site will be depending on the existing SQL objects.
I hope that helps.