The two-rule heuristic
Rule 1: dry seeds slowly at room temperature. Heat above 95°F kills the embryo. Most seeds need 1-2 weeks of air drying before storage.
Rule 2: store dry seeds in airtight containers at consistent cool temperatures. The sum of temperature (°F) + humidity (%) should not exceed 100. A refrigerator at 40°F at 30% humidity (a sealed jar with silica gel) gives the longest viability — 5-10x longer than room temperature storage.
Per Seed Savers Exchange, properly stored seeds of most vegetables remain viable 3-5 years, with cool-season crops (lettuce, peas) lasting longer than warm-season crops (corn, peppers).
What's hard, what's easy
Easiest (selfing annuals): tomatoes, beans, peas, lettuce, peppers. They pollinate themselves; you can save seeds from a single plant without worrying about cross-pollination.
Medium (insect-pollinated annuals): brassicas (broccoli, cabbage), squash, melons, cucumbers. You need isolation distance or hand-pollination to prevent cross-pollination from other varieties.
Hardest (biennials): carrots, beets, onions, parsley. They produce seed in their second year, requiring overwintering. In zones below 7, you need to dig and store roots, then replant in spring.