Hi,
Applying a theme should not do anything to your database, although it is always a good idea to make sure you have a backup of your entire site, database and all before you make any major changes to it...
A couple of other things to consider
1. What version of WordPress are you running? Are you on the latest?
2. Where are you buying the themes from? Do they have a good reputation.
if the answer to number 1 is yes, then buying a theme froma shop with a good reputation will make the process even easier and hopefully stress free.
Hope that helps,
Al