Impatiens in general would not do to well this far south and in all day sun. With a lot of watering they might be alright if they are shaded from noon on, which is the most intense sun. They also will be OK in dappled sun/shade. New Guinea Impatiens are different in that they don't do as well in light shade as regular impatiens do and prefer part to full sun. They will still require more freequent water and usually need good soil to do well.
To get a similar look of mounding plants with colorful blooms I would go with Vinca (the annual not the perennial) which thrived in the full sun area around my house. For someone with no gardening experience, probably with poor soil and questionable time to take care of watering this plant is probably one of the easiest to use. When looking for it, some places call it the Madagascar Periwinkle.
Since I don't have a picture of my own garden handy I googled for one...no affiliation with the company...
Fernlea Flowers ~ Annual Flowers: Vinca (http://www.fernlea.com/annual/variety/vinca.htm - broken link)
To the OP, your question did not have enough info so you will get a lot information that may be conflicting or not as helpful as we would like. Location was good, my garden here in the south has some big changes from the one I had up north. What works for someone else might not work for you which is why your location or your "zone" is important. It might also help to understand what kind of gardening you are up to and what you are trying to accomplish. Are you expecting to rent for a longer time so that a mix of annuals (they need to be replanted every year) and perennials (most return year after year) would be worthwhile? Can you dig up the plants and take them with you when you leave (only way to keep the more expensive perennials most of the time) and do you want to? If the rental is short term and you can't or don't want to take plants with you when you leave then stick with annuals.
Annuals that do well in sun in the south, are colorful and don't require too much garden work are the Vinca (already mentioned), Geraniums, marigold, zinnia and petunias. Each comes in many colors and varieties (some in several heights to mix and match) and would allow you to make a pretty good color splash. At the least you will need a bag or two of some form of garden soil to put in a larger hole in the ground as you plant each seedling to give the roots a break. Depending on how much clay is in your soil it may even require more than that. If it were your permanent home I'd be bringing up more topsoil and composting and all the other good gardening stuff you need to do.
If you want to put in more permanent plants you will also need to amend the soil a bit with bagged topsoil and composted manure, since it looks like your soil is not all that great. Easiest to grow perennials would be things that jkmewright mentioned, like echinnacea (Purple Coneflowers), black eyed susans, some forms of carnations. Again you did not say if you want to grow things from seed, which at this point might be a bit late for some things, or if you want to get already started plants at the local nursery. For perennials, if you can find the smallest size pot. Generally it will be the cheapest to buy and with some fertilizer and attentive watering you will have good sized plants very quickly.
Hope this helped clarify a bit on what the possibilities are... ask some more questions and give us some more info to go on and I am sure you will have a pretty garden going.
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