I've never grown Bermuda, but from what I understand, if you've got any alive in the lawn, you shouldn't need to seed. It should spread to fill in any bare spots when it's growing well.

I think the better varieties are only available as plugs or sod, anyway.

Your best source of information about turf grass is your local office of your Universtity of Arizona USDA Cooperative Extension Service since they have done extensive research (that you paid for) on turf grasses and growing them in Arizona.

Here is a link that might be useful: UA CES

2. When spring comes I plan to aerate, throw down some more bermuda seed

If the lawn was made from Bermuda SOD, you will be putting seeds of what is a pasture weed onto your lawn. There are many varieties of Bermuda, and I can't think of a really good one that comes from seed.

If you have partial coverage of the lawn area with Bermuda grass, it will give you full coverage next spring/summer with nothing more than regular watering. Water it and it spreads.

Do the "tuna can test" explained at the link to make sure you know how much water your sprinklers apply, fix any sprinkler problems this winter so you have even coverage, and follow the watering guide after that.

6. Weed control, hand picking until the soil just gets healthier and it can fight weeds on its own. That doesn't happen. If you get a thick turf of Bermuda, it will minimize the weeds, but in Arizona, water + dirt = weeds. The healthier the dirt, the more weeds, just of a different species.

What your dirt can use a LARGE dose of is soil sulfur ... it lowers the pH, frees up nutrients that are locked in the alkalinity, and does more good than anything else I can think of.

This dirt sucks up huge quantities of compost, leaving no trace until you have been at it for several years.

I recommend reducing the front lawn to the lowest amount the HOA (if you have one) will allow, make a nice low-maintenance xeriscape front and concentrate on the back yard as a play area oasis.

Here is a link that might be useful: Your Guide to Better Bermuda (ugh!)

Lots of good advice above. I agree with goal number one. Try to improve the soil. Then water and mow correctly and consistently. Then add some amendments/fertilizer.

In Phx the xeriscaping advice above sounds on target. BP Green has some low water grass posts. But, check with him on whether any are useful for as far south as you are. In this area a good lower water use grass to use is Tech Turf, an improved Buffalo grass. It needs lots of sun.

Water deeply and infrequently. Mow so as to remove no more than one third of the grass each mowing. Fertilize 3 or four times a year. To cut cost you might try getting coffee grounds for a free organic fertilizer.

I know more about the cool season low water grasses, but I did pick up some knowledge about the warm season ones during my initial research. I considered buffalo grass, but decided against it because it would have a very short growing season here and it requires a lot of sun and I have a lot of shade in the back.

If you've got Bermuda grass, it uses relatively little water, but it does use more than buffalo grass.

If you want the Bermuda to fill in and take over, you'll need to use practices that favor Bermuda. Those include mowing low and fertilizing about 1 lb of actual N per month. That may be difficult to do with an organic program. For a really good description of how to tend Bermuda, do a search for Bermuda Bible. TW wrote it and there used to be links to it here. If they're gone, you can probably find it using Google.

If you want to switch to buffalo grass, you'll want to kill the Bermuda first. If you're going to kill it organically, you'll need to wait until it warms up again, then water it well and cover it with clear plastic and keep it covered for at least a couple of weeks. The hotter it is when you do this, the better your results will be.

Once that's done, you can plant seed, plugs or sod. Seed is the cheapest, sod is the most expensive, plugs are in between. Seed is probably the hardest to establish, sod the easiest and plugs in between. The plug and sod varieties don't produce seed heads and also don't produce pollen, and those are both important considerations. The seed heads are sort of burrs and the pollen can be tough on people with allergies. I'd probably go with plugs if I were doing it.

Once it gets started, you want to mow it high and fertilize it very little. Fertilizing it more won't really hurt it, but will allow other things to grow that won't compete if it's not fertilized much. I would give it 1/2 lb N per 1000 sq ft per YEAR (note that's half as much as Bermuda uses in a month). You could bump it to a full pound a year, but I wouldn't go any higher than that.

There's somebody who posted here for a while who planted some buffalo grass in the PHX area and he kept a blog about it. Here is a link to a thread where he posts a link to his blog.

1. I have laid down some compost for the time being. Money is low right now with the move, so figure compost would be a good start to get the soil going.
Good start.

2. When spring comes I plan to aerate, throw down some more bermuda seed, a very fine compost, and a fish/sea weed fertilizer
Save money and time and skip the seed. First of all bermuda seed will not sprout until the soil temps get up into the 70s (May in Phoenix). Secondly by June you'll never know you had weak grass. You'll have grass everywhere. The fish/seaweed fert will break your bank account. You need pounds of protein per month, not micro-ounces per month. Find a source of soy bean meal and apply at 30 pounds per 1,000 square feet per month if you want it to be very nice.

3. Mowing, I bought a 7 blade reel mower and will mow weekly at 1-2"
That's too high for bermuda. Keep it at 1/2 inch to 1 inch for the best density and weed suppression.

4. Water, I plan to water as infrequently as possible. I'd say during the summer months, it'd be every week but a real good soaking. Right now, going at around once a month, deep soaking.
Too much too often is the reason you have swamp grass (nut sedge) growing in the desert. It might go away by itself with an infrequent watering plan.

5. Fertilizing, I'll stick with the fish/sea weed fertilizer to try it out for a season. I'll do it monthly.
Again, if money is an object, you'll really get much more bang for your bucks if you can find soy bean meal. Monthly apps of alfalfa pellets at 30 pounds per 1,000 square feet would be a good alternative.

6. Weed control, hand picking until the soil just gets healthier and it can fight weeds on its own.
It is grass density and infrequent watering that controls weeds. Soil health has something to do with it but not everything.