Anyone recommend a clean reasonably priced hotel right at the Rome airport?
Yep. Here's a post from Greg in Kentwood, MI.
If your looking for a clean bed, with a no frills hotel then try either the Mach 2 Hotel or the Cancelli Rossi Hotel. They are both near FCO, less than 2 miles, they both have shuttle service to FCO and the rates are a little over 100 euro per night. I stayed at both hotels and either is fine, although the Mach 2 is my preference. Both Hotels have a three star rating. Good Luck
Just a note that I received a PM from Tom who explored the two options above. They both are now 150Euro a night.