Hey, I just got back from Florida (where I have no clue what is or is not native - I just had to look and say "aint that pretty"). Your fence sounds good and if it keeps the deer out then it will be a great addition. Virginia Creeper sounds like a great choice. I haven't had much trouble with it but you probably would not want it right next to a flower bed. Poison ivy is native too but .... you know. There is also a native trumpet vine (supposed to be aggressive), a native wisteria, some native honeysuckles (which I can't tell apart from the invasive honeysuckle vine very easily), a native clematis, a native form of hop vine and some others I'm not remembering. The problem with many native vines is that many have non-native look alikes so you would have to know and trust your source and do a little research. So far I have done very little planting of vines so I am more full of ideas than practical advice.

I am assuming you realize that elephant ears can be extremely invasive in the south. They like shade (though will grow in full sun), abundant moisture, and nitrogen. They are not evergreen, so they will not hide your fence in the winter. If, after these considerations, they are still what you want, plant them about two feet from the fence and three to four feet apart. Their running roots will fill in very very solidly by next year. (Be sure your neighbors won't resent them running into their yard, because they most certainly will do that.) Think this decision through very carefully. Read some other threads about elephant ears, and know what you are getting into, because they are extremely difficult to eradicate. I know from experience. If you decide you want something else (you do, don't you?), I would recommend a nice, loose, natural hedge of evergreen shrubs. You could choose one type of shrub for a traditional look: hollies, ligustrums, cleyera (my favorite), loropetalums, just to name a few. Or, you could plant sweeps of 5 to 9 shrubs of one type together, and have different kinds of interest coming and going thorughout the year: for instance, a group of camellias (late winter/early spring bloomer) followed by a group of large azaleas (later spring bloom), followed by a group of roses (not evergreen, but mighty gorgeous all summer: the new Double Knockout Red is outstanding), followed by a group of Oakleaf Hydrangeas (early summer bloom, beautiful fall/winter foliage).....etc. See? If this is too much money to spend all at once, just buy a group of shrubs each year and gradually add to the border all the way around your yard. Plant them the correct distance from one another (as indicated on their tags), and half of that distance from your fence. For an even nicer look and better growth, dig out the grass about four to six feet from your fence all the way around, make a nice neat edge to your lawn, and then mulch. Your yard will look like a million bucks. Put your elephant ears in pots! :)

I like fewer, more sweeping curves if any at all, both for aesthetics and for ease of mowing. Notice that Doug's sketch is basically an S curve that follows the fence line and has added depth only where there are larger plants. I am not fond of random wiggles to a bed edge since it looks contrived to me, and some of my beds are basically straight with just rounded ends. You would want the shallower parts of the bed to be the 60", with any curved out areas wider as opposed to the widest areas being 60". Depending on what you find appealing, you can group perennials and smaller shrubs in large sweeps of a single kind so it has the effect of a groundcover when it has grown in some. Or you can have smaller groupings that repeat down the length of the bed. What you want to avoid is one of this and one of that with no repetition at all to give it some coherence. Which kind of repeating of plants you choose depends on what appeals to you. To figure out what you like, start looking at gardens with a critical eye. Find neighborhoods with plantings you like and wander around or visit a Botanic garden or demo garden at a nursery or look at online landscaping photos here on Houzz or elsewhere. Is the whole garden underplanted with a single groundcover to tie it all together? Is a particular color of flowers or foliage or type of plant repeated down a bed or around a yard? Are there gardens that look disjointed or don't appeal to you and if so, why? You asked about under the teees. You could use the same ground cover in both places for some repetition or use different ones if you have strong repetition elsewhere. In the corner behind the little maple on the right, you could plant something like daffodils and hostas, so the daffodils bloom before the tree leafs out and then the hostas camouflage the dying bulb foliage and are shaded by the maple while the Veronica GB will grow anywhere there is space. VGB plays well with other plants to cover the ground but lets other plants grow also, something not all groundcovers do. Some are more aggressive. You may end up with not a lot actually growing under the tree since maples tend to have shallow, dense roots that don't share space with other plants well, so I would plant any groundcover there near the drip line and then let it wander where it can. Generally, I like to keep the groundcover beneath a tree low so that the layers are distinct rather than letting the lower level of plants growing up near where the branches are. And in general in a garden that is only viewed from one side like this one, (except under trees) you will want taller shrubs and perennials toward the back and shorter ones toward the front so that sight lines aren't blocked to the shorter plants. This photo illustrates much of what I am trying to explain, though with a border that's mostly shrubs and both the border and the plants are larger than you want being perhaps 60'-70' and 15' deep with a height limit of 15'-20'. Notice that each of the larger evergreens cultivars is repeated along the bed in more than spot. Less visible at this time of year, but there are also evergreen rhododendrons repeated; one kind has 3 scattered along the length, and the other has 4 or 5. Their rhythm really shows up when they are blooming, but they fade into the background and just provide fill the rest of the year. I really value having evergreens (both the conifers and the rhodies) since it makes the bed ornamental in the winter when viewed from windows, as well as serving the function of blocking the background work area better. There are also a few kinds of deciduous shrubs or small trees that have multiples, though not at all visible when they have lost their foliage as in this photo. Towards the front of the bed are a mix of taller, shorter, and groundcover perennials and spring flowering bulbs in good sized masses which when in bloom show the same repetition down the bed. At this time of year it is less apparent since some have died back and others just blend in from a distance. There are also some individual specimens since I am at heart a plant nerd, but for me having the rhythm of repetition down the bed gives an organization that suits my tastes and rural area better than something like Doug's sketch. What you want should be what appeals to you, and only you can make that decision. Regardless, you would want one or perhaps two layers of woody plants and the rest perennials or short woodies as in Doug's sketch. Be sure you check out ultimate plant sizes rather than just what the tag says which for shrubs is often 5 years. I like the MOBOT Plant Finder where you can search for plants that have certain requirements to fit your site or you can search by name. Either way, leave everything else beside what is important to the search blank on the form.

Please, for your own sake, avoid the landscape fabric. It only does a so-so job at controlling weeds, and reduces the health of the soil underneath it - you know, the soil that your plants need to thrive. If it were my yard (where I found buried black plastic that were the 70s version of landscape fabric), I would weed, probably after a rain, turn over some of the soil, plant, and mulch, and keep mulched forever, or until your plants shade out any possible weeds. Your plants will thank you. Good luck!