CJ doesn't really care what type of site it is, as long as their making sales. It's usually the 3rd part blog site that has the regulations. Squidoo is really good for making landing pages for CJ, or wordpress or blogger if you want a full blown blog.
Most affiliate companies such as CJ and Azoogle could care less where the site is hosted as long as you can show them that you can get them traffic.
Some merchants might not like certain traffic. Be sure to read merchants' rules before you join them.