There isn;t really a proper way to raise one,
It all depends on what kind of Tamas you want and if you want more generations, or just start fresh everytime.
I, personally, LOVE the matchmaker. I don't like mating my Tamagotchis wiff other ones, unless they're both my own. I usually end up letting them grow old and die, but occasionally I'll take the Matchmaker up on his offer.
Not everyone likes a high number of Generations, me being one of them. I don't like the fact that if you get a LOT of gens., and they die, you have to start all over. With letting them die and starting over, you dont have to worry about it.
Try different things everytime, you'd be surprised at the possibilites!