[baselle]

Are you buying the seed or are you collecting seeds from an heirloom tomato? If you are collecting the seeds from a tomato, they need to ferment - harvest the seeds with the goo, let the seeds and goo rest for a couple of days in a jar (get good and stinky), then rinse the seeds from the goo, let the seeds dry, store in a cool dry place.

Several tricks that helped me:

Even moisture - no crusts
Even warmth - best place for tomato starts from seed is above the refrigerator. When you see sprouting, then move them into the light.

That weakness you see in the stems could be rot, or it could be a calcium deficiency.
Water gently, avoiding stems.
Adding calcium helps too - 2 plain Tums with calcium dissolved in a quart of water worked well for me. Let the water sit a bit so the starch in the tablet settles to the bottom.