OP, they 'shouldn't' stink. They are very clean animals that groom themselves as much as cats. What they need is ventilation and enough room in their cage so they don't have to sit in their own waste and a decent diet; that should keep the smell down with weekly cleanings. They are no where near as bad as mice. If you have bp's, you may want to look into ASF's instead of normal rats. They breed much easier and are also very clean with little odor.
That's good to know that they are not as bad as mice. We don't have BP's ....RTB's that range in size from 4-8ft and then a pair of 6-7ft Burms. I would just do ASF's but I don't believe they get big enough for our needs.