Carrots benefit from even moisture when germinating (and don't need light). I've learned from others to sow shallowly, water in and then lay a board on the surface of the bed to keep things damp and moist. After a few days, I start to check for seedlings, and remove the board as soon as they are seen. These sorts of seeds tend not to persist for years in the soil; for them it's go and grow.
Lettuce seeds (and many other kinds of small seeds) require for light for germination, so sowing them shallowly (and not covering) is important. Even moisture can be harder to maintain but it still helpful! Note that many weed seeds fall into this category; they lay dormant in the soil and only germinate when brought to the surface (hence one advantage of no-till).
Large seeds have greater stores of food and generally benefit from being sown more deeply. Beans, peas, corn etc here. For these sorts of seeds, the greatest risk is being eaten before they germinate!
Good luck and keep trying new things!