"What is the most important thing to know to grow blueberries in Phoenix?"

That it can only be done in containers. Sorry, let me be clear; THAT IT CAN ONLY BE DONE IN CONTAINERS!!!!"

Blueberries need a soil pH of around 4-5.5 (at most). They grow fine (Southern Highbush and Rabbiteye varieties with low chills (say 350 or less)). East side of house will be fine as without afternoon shade they will die in July. Ordering of blueberries is either now or in Jan. I would pre-acidify your soil which takes about 6 weeks or order Dr. Earth's Acid Soil for immediate but expensive use.
http://drearth.net/blog/products/organic-soils/acid-lovers-rhododendrum-azelea/

Plant with at least 6" from sides of container wall. I'm using half wine/whiskey barrels. 4" wood chip mulch. Never allow their shallow roots to dry out. Fertilize with an acid fertilizer after a year if the wood chip breakdown does not seem to be restocking the minerals.

Raspberries: Good luck. Raspberries have an extremely difficult time surviving in Phoenix heat. Those few cultivars that do are off flavor or literally break up into BB's when picked. If you succeed we'd all like to know. East side of house also good idea for afternoon shade. You might be happier with Boysenberry and Loganberry instead. I am trying Mysore Raspberries (to zone 10) this year as edible ground cover on my north side of the house. If you insist on trying I would recommend Bababerry (aka Southern Bababerry), Dorman Red, Caroline Red, Fall Gold but you should consider them experimental. There are a couple of more that are zone 11-12 but Australian varieties I can't find here.

Blackberries: A few cultivars seem to do well to OK here.
http://cals.arizona.edu/pubs/garden/az1450.pdf
http://www.greenthumbjeff.com/2010/05/growing-blackberries-in-arizona/
Roseborough and Brison (a couple weeks before Roseborough) do well. People have said Ouachita and Triple Crown (both thornless) will do OK here but I have yet to see their fruit.

It will be interesting how the city and your home insurance (fire) likes your front yard full of wood chips. I have been wanting to do that myself. Think tall hedge out front. Only I'm thinking 18" deep.

If you are interested in fast berries...might I suggest grapes. And fast fruits...melons. They do well here and in full sun, or near full sun.

Here is a link that might be useful: Blueberry soil mix

Thanks for your help!
I am building a block fence around the yard, partly to hold in the chips, partly to keep food-moochers out, partly privacy. My neighborhood is old and rundown, so I don't think anyone will care.
I appreciate the recipe reference. I hadn't realized they couldn't go in the ground.
For the berries, I will be amending deeply, with a sort-of-hugelkultur method I made up in my head.
I didn't have good luck with grapes in the past. The &*&^** birds got to them. I tried all kinds of enclosures for the clusters, but I must hve been doing sonething else wrong. Do you think they would survive against a block wall facing South?

For blueberries, You're going to have a problem using our highly alkaline tap water here.

I read an article a while back about blueberry growers in central valley of CA adding sulfuric acid to their irrigation water- something you probably wouldn't want to do. The profit on blueberry production has made that extra step worth it, I guess.

It is not that bad. You can add a cup of apple cider vinegar to 5 gal of muni water and the pH will be around 4.5. But that doesn't matter much. The pH buffering of water is negligible. That of soil immense compared to water. So the pH of the water does not change the pH of the soil. Unfortunately our calcium ions will over time. You can try washing the container soil out say once every 6 months. Additionally acidified water should help carry the monovalent and divalent salt ions down and out rather than bridging to the soil. Or better yet, use di$tilled (although AC and refrigerator condenser water is free) or rain water.

If by they you mean grapes, some cultivars will do amazingly well up against a block wall facing south: Thompson Seedless (green) and Blueberry (aka Glenora I think, also seedless and purple hopefully in our temps). I have yet to find a red seedless that does well in full sun. Also while Blueberry is amazing in growth, my experience is only 2nd leaf and therefor no fruit yet. That seems to be the experience of others. So until someone starts showing pictures of their bounty I can only be very hopeful.

What do you think of the calcium filters for the hose?

I ran across this video--I had seen it before and was reminded of how good Karis is--that in turn reminded me of this thread.

Here is a link that might be useful: Growing Blueberries in Phoenix