I just think you have to hold out and go rat all the way. The fact is most of the stuff your parents think is true about rats (biters, messy, stinky, etc) is really more true of pets like gerbils and hamsters. Rats groom themselves like cats, can be litter trained, the girls smell like grapes, they never bite when healthy and properly socialized, can learn their name and tricks like a dog or cat, etc, etc. They also just bond and show affection so much more because they are so soo much smarter. All pocket pets are cute, but none of them hold a candle to rats, though mice do come closest. My dwarf hamster bit frequently, but I don't know if they all do. I have 5 adult rats and none of them bite, including the two that have had to get antibiotics twice a day. Just do your research, be persistent, and make your point. Show them that what they think about rats just isn't true, it's all a big myth, like those people who think it's a good idea to have an iguana on a leash because they saw it on tv, alot of our view of animals come from media and are not at all based in fact.
A cage topper should do fine with two rats. How much they cost depends. They're not going to cost you more than $15 to buy, but if you're not careful where you get them they can be very expensive in vet bills if you get them somewhere that doesn't take good care of them. Also before you buy any cages or supplies retail always check the paper, garage sales, ebay, craigslist etc, and look in petstores for slightly damaged floor models (got a perfectly good $120 cage for $50 this way once.) Pet supplies are expensive when you get them retail, but there are a lot of alternative places to find them.