Assuming that you have shared hosting, if your account has Fantastico or Installatron, just get a new domain on your account. Leave the root blank and in subdirs that won't get crawled (your root will get crawled based on Whois info), just start pushing buttons and installing CMS in various subdirs and play with them in a low-consequences environment. Likely one of them will seem to make more sense to you than the others.
>>Is it difficult to incorporate your current site into a CMS
It depends on what you mean by "incorporate" and what's on your site currently. It should be quite easy to modify the templates to look like your current site. For simple text/image pages, you'll likely have to just copy and paste. If you have lots of pages, you could write some sort of script to try to import the page-specific info and update links.
>>as well as dangers to look out for
- Duplicate content. The directory pages, archive pages and the many ways you can access a given page in many CMS can lead to duplicate content problems. You can control this with a robots.txt, judicious use of noindex and other such measures.
- HTTP response codes. Most CMS that I know have finally gotten this sorted out and a page not found sends a correct 404, but sometimes CMS serve up custom "404 pages" that actually return a 200 code.
- server load. If you have tons of traffic and your server is struggling to keep up with the load serving up static pages, you'll need to upgrade in order to handle it. If you're just serving up a couple thousand pageviews per day, any shared hosting account should be able to run most CMS.
There are probably a hunder other things, but I'm getting sleepy!