My preferred tomato to grow has typically been some cherry type variety which I've been growing from seed from a plant a friend gave me a few years ago.
To harvest tomato seeds, simply cut the tomato in half and squeeze out the goo into a strainer, rinse the goo off and then place on a paper towel to dry overnight. Once dry scrape them off into a paper bag.
Apparently you can grow tomato plants from a cutting which I am yet to do successfully.