You've actually posed several different questions.
The general answer is, yes, you can certainly use store-bought veggies. Keep in mind, though, that they are not the best quality, and your pickles etc. will reflect that. Buying organic in a supermarket will have no significant effect on that.
You're better off buying at a farmer's market. I see you're in Seattle, and there are several such markets operating there. It's well worth the effort seeking them out. You get farm-to-table freshness. The veggies are actually field ripened. And you're better able to buy in quantity. And at the peak of the season.
Wax on cukes is a cold-storage technique. Cucumbers sold in season do not have that covering. Waxed cukes are also slicing types, and the best pickles and relishes are made with pickling types.
We're I you I'd start by doing a search, here, under canning and preserving. JustPJ has written several how-to articles, and they're a good beginning.
I'd also be sure and get a copy of the latest Ball Blue Book, which is the bible of home canning. And, when you're ready to start, buy a canning starter kit, which will have everything you need except for the canning kettle and jars. You'll have to buy those separately.
One cautionary note: Canning (as well as other food preservation techniques) can be addictive. So bear that in mind as you start your new culinary hobby.