Welcome to the desert and to the forum!

You can get a reel mower, or for that small of an area (assuming that it is near your house) you might consider one of the electric mowers. It's really how much muscle you feel like putting in to it - if I had to depend on a reel mower, the lawn would be over grown all summer, lol.

Bermuda does realllllly well in the summers here, too well for my tastes as it's very hard to contain and keep out of other plantings. You'll also have to watch for it sprouting up in other places. But if you decide you want a green lawn throughout the year, I know that some folks over-seed an annual rye with manure and water it in rather heavily.

Other people will likely give you good weed 'n feed ideas; having animals, I would only consider using corn gluten, were I to have a lawn.

Best of luck to you, you're about to see a really nice change in the weather, enjoy!

Bermuda grass doesn't like cold temps, and it will go dormant over the winter. That would be a good time to add topsoil and manure to level out the lawn, and as mentioned, overseed with rye grass if you'd like a green lawn over the winter (you might rather have a break from mowing!).