For the initial sign up to Commission Junction you can literally use whatever site you like in your websites, google.com, madeupsite.co.uk; anything you like.
At the point where you begin applying to merchant programmes is where you might need to be a bit more careful - although not in all instances.
The longer tail and rarely some large merchants will have auto approve applications to their programmes. Most large or well known programmes will have basic auto acceptance criteria which is more related to your listed location, publisher rating etc.
Larger programmes will often manually review applications, either by the Commission Junction account manager or by the merchant themselves. This will always involve looking at the site listed. CJ don't like blogs hosted on a blog network such as Wordpress.com although self hosted wordpress.org sites are fine for example. If you don't have your own site, no problem. Just make sure you list your promotional activity within your publisher special terms and conditions and ensure that this is compliant with the merchants terms and conditions.
In these cases when you are rejected it is usually possible to speak to the account manager or merchant to make a case. It doesn't need to be entirely legit. Sometimes simply saying your site is under construction and you need to pick up links is enough.
Be aware that the 'network quality' team at Commission Junction will review your account, sales and promotional methods at regular intervals throughout the life-cycle of your account.