The easiest I know (and a staple of my garden) are nasturtiums (which are a big hit with our local hummingbirds.)

Popular but considered invasive.

Any ideas for an apartment dweller would be welcome, too. I've been thinking I should start something.

What you choose to plant will depend very much on local conditions -- climate, precipitation, sunshine, local animals and birds, pests, etc.

I do a simple container garden on my deck every summer and choose an assortment of flowers and herbs that are easy to grow and each year it gets a bit bigger.  My deck has a couple of different lighting zones, which affects what I plant (and where)  Away from the house along the front and in the middle of the deck, I get full sun.  In the shadow of the house I get full or part shade, which makes a difference, so I typically plant a more shade-loving mix near the house, e.g. in the kitchen windowboxes

Just a few planters and baskets can make a big difference in your enjoyment of an outdoor space.

Things to remember:

1. Plants are pretty simple.  They require:
   • light
   • water
   • food
   • protection from diseases, predators, and damaging conditions (drought, high winds, etc.)
   If you provide them with those they will generally do well.
2. Start with a few choices that are basic, robust, and inexpensive and see how you do before adding more.  Ask at the nursery for recommendations that are appropriate for your area.
3. Use good-quality soil (i.e. if you are going to grow in containers, use a good potting mix -- don't just buy cheap topsoil) and apply fertilizer periodically.
4. Container-grown plants have less recourse against drought than plants which are in the ground, so water regularly.
5. Many annual flowering plants require moderate maintenance, such as removal of blossoms before they go to seed (aka "deadheading") to keep the plant in bloom.  If you don't know, ask when selecting plants whether you should cut or pinch off blossoms after they peak to keep the rest of the plant going.  Also, ask for plants that will remain in bloom through most of the season.

I live in Southeast Alaska, and my climate zone is similar to coastal BC and the Pacific Northwest region west of the Cascades.  If anyone is a beginner from those areas and wants suggestions for what works well in my containers, post here or PM me.

"Any ideas for an apartment dweller would be welcome, too. I've been thinking I should start something."

Well. you might want to try a couple of these, but they're not exactly giving them away.  You should be able to get some simple containers and potting soil for a lot less.  

As for what you plant, that's entirely up to you.  Tomatoes are always good.  Bush beans will work.  Viney things, like squash & cucumbers are out.   Same for corn.  Greens like spinach or swiss chard would do well, as would any sort of peppers.  

If you're after flowers, as I mentioned above -- I'm going to try wildflowers this year.  Should be low maintenance, and it doesn't turn out right, I can always pull out the weedeater and that's that!

This link and it's accompanying links might be of help to you.  

there's only one way to find out...

You could shell out the money to have it re-sodded.  If it's not a huge yard, it shouldn't be all that bad, probably a few hundred or so.

I don't have much intention of keeping a lawn when I get a house. Plenty of houses around here have large fences all the way to the sidewalk and you can just put a nice tiled courtyard effect inside of that. We have dogs so I don't see much sense in trying to beautiful the back in a typical way. I'd like to go for a wild garden type effect that looks basically good in any non-dead state. Sorry no helpful lawn hints:)

It is easy to buy small plaster models of what you think life is like.