Current recommendations call for pressure canning of plain tomatoes. The acid level of today's tomatoes is not high enough for safe waterbath canning. (And I know, some folks have done it that way for years and years and they haven't died. Yet.)
Do go get the Blue Book, *do* follow directions exactly. The chance of your canned jams or even the tomatoes developing botulism is minimal, but you probably don't want to take any chances with a toxin that KILLS YOU DEAD .
Canning is great fun, lots of work with lots of rewards--nothing finer than lining up those jewel colored jars on the counter!
If you have any questions about canning, you are welcome to pm me. I have canned many a jar in my life, I love doing it.
PS: This is one instance in which you don't have to listen to your mom. Can according to current standards, and you won't make any body sick, unless they eat too much of your delicious jams and jellies.