Some places that sell storage foods also sell canisters of “survival seeds”. Don’t bother getting those. They generally have way too few seeds, in varieties that may or may not grow well in your climate, and the species those canisters are filled with tend to be heavy on the green leafy stuff and light on starches and proteins.
My suggestion is to start by testing lots of varieties now, so you can identify what does best with your climate and growing style. Non-hybrids are generally better for seed-saving, but make sure you either know how to keep the seed pure, or know enough about plant-breeding to know what you’re selecting for.
When you identify a good variety, start socking away extra seeds every year. With some foods, such as tomatoes or squash, the seeds are abundant enough you can easily save 10 years worth in a single season. Others, such as corn or beans, are a bit trickier, simply because the seed is also the crop. For those, I suggest planting a row or two specifically for seed. If growing dry corn, save a few seeds from each ear, as corn is prone to inbreeding depression. Be aware of isolation distances, and plan accordingly.
Vegetables that are grown from tubers, bulbs, cuttings, or slips, are harder to save. It is possible to get true potato seed (TPS). I recommend Cultivariable for that. They also have articles on how best to grow potatoes from true seeds. I have not been able to find a reliable source of true seeds for things like garlic or sweet potatoes, but I keep looking.
When choosing which varieties to grow, pay attention to things like storage life as well. Some varieties of squash can be stored in a corner of the basement for over a year, with no loss of quality. Others start to go bad after a month.
Don’t neglect spices and culinary herbs. The late great Jrandomfreeper used to rant about the dangers of palate fatigue. If a person isn’t getting enough variety in their diet, it becomes harder and harder for them to eat. People have quite literally starved because of this! So, lots of herbs, lots of spices. Look into things like sorghum or sugar beets to grow as sweeteners, too. Also, don’t ignore oil-seeds, like sunflowers, sesame, or flax. Fats are essential in a survival diet.
As for how many of each type to save, my only suggestion is “more”. As you test varieties, you’ll get an idea of what kind of yield to expect. Use that to calculate how many plants you would need to supply you for a year, add 10% and double it. That’s how much to grow per year, so you’ll have a buffer if there’s a bad season. But, save seeds beyond that number, so you have them to share or barter with. Seeds are tiny. You have room.
When storing seeds, dry is better than humid, and cold is better than warm. When taking a tour of the Baker Creek warehouse, the manager there told me that seeds maintain their viability best if the temperature in F and the % humidity add up to less than 100. That said, don’t get fanatical about it. I have seeds that sat in a corner of my bedroom for 20 years, which at times had a humidifier going so strong you could see the steam, and a space heater 4 feet from the seed boxes. When tested, they still had germination rates over 90%. Seeds want to grow. It’s what they’re made for.
I don't even bother with seeds for those.
For potatoes, I bought Kennebec, Superior, and Red Pontiac.
The Kennebec (bred in this area) and the Red Pontiac both do VERY well in my garden and I figure there is no need to try with seeds. They both keep very well and provided me with enough seed potatoes for each year's crop. I gave up on the Superior.
For garlic I have Romanian Red, Music, and Great Northern White. They must have slightly different growing preferences because one variety will out perform the others in different years. However, saving the biggest cloves for next year's crop is far easier than trying seeds, IMO.
Onions are also prone to inbreeding depression. The recommendation is to leave at least 20 plants for going to seed.
Next year I am going to try an experiment of starting onions from seed and letting some grow for my crop, and crowding the others so they become the year after's onion sets.