Mice smell, but rats really don't, especially when properly cared for. Hamsters stink and ferrets stink, and yet both of them have better reputations than rats. Rats don't bite or smell or scratch nearly as much as the former. Rats, in my opinion and that of many others, are some of the cleanest pets you can have. Domesticated rats do not smell very bad. They don't even smell as bad as dogs. And nope, no one here is trying to sell you rats. I don't sell rats, and most people here do not. You're actually not allowed to sell rats on this website. If someone were doing that they would probably get banned, because rat forum discourages breeding rats and it is forbidden to use the website to do so. The closest this website comes to that is the section for rats who need homes - and even then, you're not allowed to sell them. It's strictly adoption. We're really just here to talk about our pets.
Male rats have a more distinct smell than females, but it's really not that bad. It's nowhere close to the smell of a mouse or a ferret (realizing that ferrets are not rodents, but I still hope you get what I'm saying). Rodents in general are actually pretty clean, as they groom themselves constantly. Rats are on the top of that cleanliness hierarchy, spending at least a 4th of their lives grooming themselves. Now, if you let any creature wallow in its own filth it will stink no matter what. But, if you clean the cage at least weekly (I clean mine two times a week at least) and change out their bedding regularly there won't be a bad smell. I use aspen shavings in their litter box and it makes them smell very fresh and clean. A rat will usually take on a hint of the smell that their litter has, so if you choose aspen and change it every third day or so they will smell very fresh.
And, as a rule of thumb, if you don't like the way that an animal smells, the odds are they do not either. When my girls get stinky (which is rare) it means I've not cleaned their cage in a while. If the smell is too strong it can actually cause them health problems, like extra sneezes. In the wild it wouldn't be as much of an issue, because they would have a bathroom area that was further away from general living area (and their waste would be absorbed by nature), but in captivity we keep them in cages where everything is inadvertently closer together and therefore more concentrated. There's nothing wrong with keeping them in cages, that's NOT what I'm getting at. You just have to clean their cage regularly, or else it will smell. Just as a human must take baths and wash their clothes, you have to help them maintain their living space and they will do the rest. Like I talked about, I use aspen in their litterbox to keep them smelling crisp. I also use fabric and bath rugs to line the cage. These are washed regularly and are pretty easy and cheap to maintain.
Best of luck in your endeavors. I'm not sure how old you are, but I'm 19 and until this year I was in a similar situation. After our family cats died, we stopped having pets (with the exception of fish). I had to work my way up and demonstrate that I was responsible enough to commit myself to the care, keeping, and health of a warm-blooded animal. Now an adult, I have two rats and my family (though initially very skeptical) adores them. Remember that even if it's hard to convince your parents now, it will only be a short time before you are able to get them on your own! It may seem like a long while of waiting, but it will fly by before you know it. And, there are plenty of things you can do in the mean time, like volunteer at a rat rescue or general animal shelter.