First off, I can't believe all the yard advice you are getting from people who live in northern climes for a yard in Orlando. You people have no idea. We mow our yards twelve months a year. The grasses and plants are totally different.
I know you want to save money and all, but replacing your yard is about the nastiest work that there is. BTDT. I would talk to several landscaping companies to get an idea as to how much they would charge and then figure out how much it is going to cost you to do it. Like most contractors they get their materials and labor cheaper than you and I think you will be surprised at how little difference in cost there will be.
If you are determined however here is what to do..... Use Round-Up on the entire area that you want to replace. Wait a week and do it again. It will usually take 2-3 weeks for the grass/weeds to die completely. You will then need to remove all the existing grass/weeds (Hot, nasty, back breaking work) and discard it. DO NOT, DO NOT till the soil. This will just stir up old weed seeds from below. The dirt yard will now need to be treated with a 'pre-emergant herbicide'. This will prevent weed seeds from sprouting up later through your grass. It is very important that the removal, herbicide spraying, and installation occur right after one another so that the weeds do not have a chance to start to grow. If it takes a week to get the grass down the weeds will just be cemented under your new turf and you will never get rid of them. There are so many growing things in the soil here in FL that it is important that the soil be as "sanitary" as possible when you put down the new grass. This will also eliminate the bugs and insects that the moles are going after in your yard. Once the bugs/insects are gone, the moles will just stop coming in your yard. You can usually buy St.Augustine by the pallet from landscaping companies. Absolutley do not buy plugs and attempt to do your front yard. It takes months for the plugs to grow together and in the meantime the weeds fill up the empty spaces. BTDT, too. Backyard or smaller spaces OK, but not your front yard. Water the soil good and then install the new grass (Did I mention hot, nasty, back breaking work) Only one rule here: Green side Up
. You have the right idea about installing a sprinkler system. Most landscape companies will not even install St.Augustine unless you have a sprinkler system. With one though they will warranty, yes warranty, the installation and that your yard will survive and look good or they will replace it.
St. Augustine is the best looking grass and may be required by your HOA. It requires a lot of work and needs to be treated as a growing plant not just like a pasture. You will need to have a regular maintenance program. Fertilizing, herbicide, watering, correct cutting (use the highest mower setting possible). The quickest way to stress St. Augustine grass and make it susceptible to cinch bugs and heat is to cut it too short. Hint: Ask the guy with the nicest grass in the neighborhood what he does to keep it up. He will be glad to tell you.
Good Luck and if you have any other questions, just ask.