I will also advocate a pet rat over a pet mouse. Female mice don't smell nearly as bad as males do. But, mice are small and they are fast. They won't ever be the cuddly, squashy, loveable bundle of fuzz a rat is.
Now, you can keep a single rat, as long as it has plenty of toys and time each day with you. My daughter had a male rat named Remmy, and he was just fine by himself. She got him out each morning before school, every afternoon after school, and for some schmoozing before bedtime. I had no idea before she got him that rats could be so lovable. He cuddled and licked and gave kisses. He'd beg for treats and hide if he was naughty. She had him for 3 wonderful years, and still has his son and granddaughter today.
Gale