Theda K. put it best, so I will give her credit where credit is due and copy her answer down here for you to consider when it comes to that question of "Which rat?"
Unless you're planning to breed rats, you definitely have to keep just one gender in a cage. I've had both males and females, and there are several differences.
I always let my rats run free in my home, and male rats had the disturbing habit of leaving a scent mark "trail" everywhere they went. I didn't quite care for the little droplets of urine, especially as they crawled on me.
Male rats also have a slightly musky odor (though nowhere nearly as strong as ferrets). They also have large testicles right under their tails...they're pretty obvious, which can make for interesting conversations with visitors.
Other than that, male rats are really cool. They're cuddly, relaxed, and kind of lazy. They're bigger than females, which just adds to their cuddle factor, and surprisingly affectionate.
You do have to be careful when housing male rats together. I was lucky enough to have three males that were brothers, and raised together, so having them in one cage was no problem. But it's difficult to introduce two adult males. Female rat introductions can be difficult also, but it's a little bit easier.
Female rats are probably my preference. They are smaller and definitely more active than the males, but this makes them, in my book, a bit more interesting. Females are full of personality.
It's also funny when they go into heat every week or so. They get all jumpy and flirtatious, doing little scamper dances. And if you or another rat tickles their lower backs, they arch their backs and wiggle their ears.
Female rats' personalities also make them ideal students. Mine loved to learn new tricks, and always wanted to interact with me. The main downside of female rats is their propensity for getting mammary gland tumors. Of the 7 or 8 female rats I had, almost all of them died because of their tumors. It can be extremely costly to have them removed (I did that once), and it's heartbreaking to watch them endure.
Whichever gender of rat you choose, you'll be sure to have a great time with your new companions.
