(1) I like Baker Creek Heirloom Seeds, at rareseeds.com. It's a small family business, started by a young man when he was 17. They put out a nice catalog with gorgeous pictures, and have a wide variety of many vegetables. (I had no idea there were so many kinds of eggplant, for instance.) We've bought from them for three years now, and always gotten our seeds very quickly. Prices are kind of high, so we buy common varieties at the local seed store, and then get the uncommon stuff from Baker Creek.
(2) I'd probably put raised beds on the ground. They shouldn't dry out as quickly there as they might on your deck, and you can save your deck space for other things.
(3) I think they're all fairly easy, so I'd start with what you like. Don't grow things you don't like to eat. That seems like "duh" advice, but you'd be surprised how easy it is to get excited when it's February and you're looking through the seed catalog and thinking, "Hmm, that Japanese fuzzy melon looks really cool; maybe I'll grow that and find recipes for it." Save experimentation for later, when you've got some gardening experience, or you'll just get overwhelmed when it's 95 in August and you're out there weeding around something you're not even sure is food.
For easiest plant ever I might nominate Swiss chard. You can plant it early, it doesn't bolt in hot weather like spinach and most other greens, and it'll last until a hard frost in the winter. You can eat from a few plants for several months. Most root vegetables are pretty easy, too; just plant them at the right time of year (most prefer cool weather, but check the package) and dig them up when they're ready. Green (or wax) beans are also very easy; plant the bush varieties if you don't want to have to give them something to climb.
Tomatoes are a bit more advanced; they need to be staked or trained up trellises, and they can get blights and diseases. Perennials like asparagus and most berries are more complicated too, but if you like them, give them a try.
(4) We compost, and when we had close neighbors, I honestly don't think they loved it, but they didn't complain. You can do some things to make it as inoffensive as possible. Put it somewhere your neighbors won't have to see it every day, even if that means building a little privacy fence around a side or two of it. If you put things in it that might blow out, like shredded paper, make sure to spread some soil or something over the top so nothing blows into your neighbor's yard. If you add "hot" materials like grass clippings, layer them with plenty of "brown" stuff like straw or shredded paper, so they won't rot in a big lump. Good compost doesn't have much odor, but a pile of grass clipping by itself sure does.