I've been collecting and replanting tomato seeds for a few generations now. No issues.

Seeds should be kept cool, dry, and dark.

What you want is "Heirloom" seed. Heirloom varieties have been bred for stable offspring traits. Hybrid seed produces unreliable offspring traits, no good for saving seeds. Heirloom varieties produce the same offspring as the parent stocks. Cross pollination isn't much of an issue with tomatoes. They like to pollinate themselves

You can literally spend a lifetime researching the answers to your questions. Here is a very basic primer on the subject.

OP = open pollinated. This means that this is a population of related individual plants. These are produced by growing the parents in a large field and taking all the seed. Outcrossing, off types and variation is normal. Relative uniformity is maintained by roguing out off types.

Inbreds = are genetically mostly uniform (above 98%). These are used to produce OP's or F1 varieties . These are created by self-pollination, sib-pollination or double-haploid techniques.

F1 = A cross from two inbred lines. Most varieties grown from seed will produce fertile gametes with very few exceptions. Seed can be produced if you know how to. The reason F1's exist is because of heterosis or hybrid vigor. This makes the plants of some species (if bred corectly) healthier, more uniform, and produce more than OP or inbred lines. Saving seeds from an F1 will created and F2. F2 is the generation of maximum variation and the resulting plants will all be genetically unique.

Confusion of fertility of F1's: Sex expression in plants gets complicated. All male or all female plants are common in nature. Plants can also have separate male and female flowers on the same plant and all sorts of varietions. You can also change the sex expression of a plant with the application of some hormones. Plant breeders often take advantage of these diffences in variety development. Only varieties that have an odd number of chromosomes (like seedless watermelons) are truly sterile.

Saving seed - each species has its own techniques to successfully save seed. You'll have to research how to do it for everyone. Some are very easy to do like cantaloupes. Others can take specialized skill to save like lettuce.

Storing seed: Each species has its own storage requirements. You'll want to look up the requirements for each one. There are wide ranges of temperature and humidity. Some species can be stored for decades. Other species are only viable for a year.

Economics/risks of saving your own seed. Yhis gets extremely complicated fast as well. Seedborne diseases, pests, genetics etc all are parts to consider. There is no one size fits all answer.

If you want eventual independence, look at perennials.

Currently growing: tree kale, rosemary, sage, chives, bay, spear mint, jerusalem artichokes. Looking to add walking onions next.

None of them cost me anything beyond initial purchase. If you can find people willing to swap it would help a lot too.

This is BigSeed propaganda for sure 😂

Store bought hybrid seeds will either be sterile or make bad plants (here they are always labeled "F1" on the bag), and I don't know for GMO seeds, as they are forbidden in my country. But all other seeds should be viable for reproduction in theory.

I've made some of my own seeds, adding new species to my collection each year. I've had easy successes with some species (tomatoes, cucurbitaceae, brassicaceae, most flowers), but no luck with others. I suggest you try and learn what works.

For whatever reason, cross pollination does not seem to be a problem after a few years. I guess it will eventually become one with time if I keep having multiple varieties of the same species. Again, try and learn.

As for storage, I put my seeds in little origami bags made of newspaper, and keep that inside at room temperature. It might not be ideal for conservation but it's easy and works well enough.