For your size lawn, and since you have a rider, I'd recommend a tow behind sprayer. The one that I got was the
Fimco 20 gallon sprayer, available at Tractor Supply. I liked this one because the price wasn't too outrageous, and the capacity allows me to fill it once or twice, depending on what I am applying. It comes equipped with TeeJet flood nozzles, so you can vary your nozzle based upon what you're spraying. For herbicides, liquid fert, humic acids, pesticides, it's a great all around sprayer. The spray nozzle is nice as well, since you can leave your sprayer parked, dismount, and spray manually. This works great for steep slopes, and hard to reach places.
If you wanted a walk behind sprayer, I would suggest the Chapin 97900 20V. There's a good thread on the member's experience with this sprayer. I've gotten good use out of mine over the past few months.
For granular applications, I'd recommend the Earthways 2170, and it's your choice to get the deflectors or not. I didn't want to pay another $60 for them, so I opted not to. I was a little bummed that it wasn't standard issue on that model, but it's not a big deal. I will say that if you have a Site One nearby, and you give a Lesco spreader a push, you'll fall in love. I was having buyers regret when I gave one a push a few weeks after I got my 2170. They're nice, but very pricy.
Get a 2 gallon sprayer, and
outfit it with a proper sprayer wand.
Here's a thread with links to most of the products that I mentioned above.
As far as your yard goes, keep in mind that in your area, you're nearing the end of the growing season for bermuda. At most, you've got another month, maybe less. Unless you want to overseed for the winter with PRG, I'd focus on getting a PreE down, controlling the weeds for the winter, prepare for spring, and become well versed on
The Bermuda Triangle. Come spring, you'll be ready for your first app of fertilizer, Celsius on the weeds that came through your PreE, and ready to rock. You're gonna love the way your lawn looks, I guarantee it.