I realize you are trying to landscape without making a large investment, but I think in the meantime you are going to have to research what grows in your neighborhood, what would be effective and appeal to you. First - don't spend money or time on plants until you've made any improvements to your soil that might be needed, it's not a step to skip. While the yard soil you currently have may be satisfactory for many types plants as is, it won't be appropriate in a container - essentially all products sold for containers are soilless and with reason.

If you are looking for trees to start, you might consider citrus, many will come true from seed, although most will have thorns where the grafted purchased seedlings do not.

Hazelnuts (filberts) will acquire a deep embryonic dormancy if the seed is allowed to dry. Best chances of some germination follow 2 - 6 months of stratification (moist chill of 40F). Do the trees even grow there? I don't see where they are at all common in your state - those nuts you bought are probably from Oregon.

Almond - Prunus dulcis. Seed - requires 2 - 3 months cold stratification and is best sown in a cold frame as soon as it is ripe. Sow stored seed in a cold frame as early in the year as possible. The seed can be slow, sometimes taking 18 months to germinate.

Here is a link that might be useful: Hazelnut distribution

Eh, I figure hazelnuts are a longshot, it's just something where the seeds only cost me $.30 or less, and I can grow spinach or something in the pots while I'm waiting for the hazelnuts to sprout.

I'm going to fill the pots half full of proper potting soil, and I may well put the plants in the ground before they grow large enough to get all the way through the potting soil to the dirt

So, I should stick the hazelnuts and the almonds in the fridge, in damp soil or something, for at least 2 months?... Or do you think the outside weather might fake it for cold stratification for the almonds?...

Two months would be the minimum amount of time for a moist chill, I don't know what your temps will average over the next weeks, I wouldn't think quite that cool - and not that moist. Here, they would be moist and cool long enough - but I've only visited your state, not gardened there.

If you do use your refrigerator, use a sterile medium in a zip lock bag or similar container and date it...sterile medium like moist sterile vermiculite or moist sterile sand.

Actually, "moist" we've got, it's the winter rainy season. I haven't had to water my back yard in weeks. But "chill", not so much, I think we're still running in the 70s.

Do you think water crystals would work as my sterile medium?

I don't know, really - no experience there. I've only seen them used as a soil additive for plants with roots.