Dan, there's no need to plant more than 1 of any particular type of tomato (other than the reason that you love that type and want lots of it). How many plants you need is totally dependent on what you want to do with them... do you just eat them fresh? Do you want to can tomatoes and make tomato juice and sauce and salsa (like I do) ? Do you eat a lot of little cherry type tomatoes in salads and for munching? It's really something you have to kind of work out over a few years of trial and error, but just for a starting point:
I usually grow 12-14 plants in my garden, which include a couple of small-fruited types, and I have more than plenty to eat fresh (LOTS of BLTs!), plus making roasted tomato sauce (about 30 cups), salsa (maybe 3 dozen pints), and tomato juice (about 12 quarts), as well as some peeled tomatoes frozen for adding to chili and such.
Being overcome by too many tomatoes is sort of a dream of mine...