Clusia Rosea is the easiest hedge or tree I have ever planted.

https://www.south-florida-plant-guide.com/clusia.html

What about Sea grape. It is native in your area and a beautiful plant. http://gardeningsolutions.ifas.ufl.edu/plants/trees-and-shrubs/trees/sea-grape.

It's going to be easier to maintain as a strip/border bed that is separate from the lawn than it is as individual plants along the fence. You prefer "not to have it be too deep," but realistically, if you have screening plants, they or their canopies take space. There will be height and size. It does not look good to have large plants that are pinched tightly into a bed. The minimum width of such a bed is probably going to be in the 5' or 6' range .... not 2' or 3'. It's going to look better if the bed is deeper at each end where it connects with the side lot line bed or ties to the side lot lines. At each end where the bed is deeper, it makes sense to have even taller plants (which could be shrub forms with their foliage extending to the ground.) For the main run, I'd suggest tree form large shrubs (with the lower foliage removed) so as to divide up the length of fence, not cover it entirely, Tree forms would make the yard seem more spacious as the ground area would not be filled with foliage, whereas it would be with shrubs. I would recommend filling the bed below solid with groundcover so you could look at a cushion of green that never needs mulch again, as opposed to a bed of flat, dry, brown mulch the must be refreshed annually.

A general concept or arranging...

Ooo that's a very interesting idea. I like that a lot!!! Thanks so much for putting that together! Not sure if you're familiar with Central Florida but if you know of any good shrubs and trees that would fit that type of layout nicely, I'd love to hear from you!

Magnolias grow quite nicely in the area. I guess you don't want an oak tree that grow like crazy, but if you keep it trimmed it won't get out of hand.

I live in Tampa! :-)

The first thing that comes to mind for the end shrubs is Podocarpus 'maki,' which is readily available here. But it could be other large shrubs, too, such as Viburnum odora.

Choices for the tree forms ... there is the ubiquitous crape myrtle --'Catawba" would be a nice color that didn't get too large. Also, chaste tree (Vitex), Japanese ligustrum (though these get quite beefy), Oleander 'Calypso'. If you're into palms, it could be a row of Pindo palms as they are not too tall and very cold hardy. But that would be a row of single trunks which I don't think would be as good looking as a multi-trunk form.

For a groundcover, Liriope muscari is one. It could be a variegated version. Many people use the ferns that grow just about everywhere wild (which I believe is just Boston fern that has escaped cultivation.)

In your daily travels, look around and see if you notice anything that could fill the bill in the scheme you're trying to accomplish. I'm sure there are other plant options.

I've been to Orlando and seen what is planted there, based on that there should be all kinds of things you can use in Tampa. Visit some display gardens and garden centers for specific ideas, viewing the shrubs in person you can see what you like the look of and use that as a starting point. Instead of checking out suggestions made on the web and then finding you don't like some of them when you seed them face to foliage, as it were.

some ideas using tree-form Japanese Ligustrum:

That looks like exactly the type of thing that seems lower maintenance and naturally the kind of form I'd like! Sort of like what Yardvark and others were proposing - to have the tree trunks below with the foliage above the fence... I like that a lot! My wife is doing research on all this stuff - I'll try to make sure to keep you guys updated as it comes along!!! Thank you all!!

What about Indian Hawthorn?!? It says it's an evergreen but I'm not sure I've ever seen this in person:

One more thing if any of you happen to know - I'm seeing various forms of this Japanese Ligustrum that is kind of confusing. Something about a "Texanum" version and something about Privet. You can see I'm really an expert here but is this the one I'm looking for? I'm seeing differing information about the height and spacing on these things which is making me think there are bunch of different species going around...

https://paradisenursery.com/product/ligustrum-japonicum-texanum/

This is what I'm going for:

A difference between people and plants is that the former are difficult to clone while the latter are easy. On account of that, when individual plants which are outstanding or unusual come along, they are often named and cloned and marketed as such. They are not different species, but different individuals, that are replicated in great numbers. So you will find some named Japanese Ligustrums that have somewhat different characteristics from the straight species. There is one that has whitish/yellowish tip growth, for example. These named varieties are collectively called cultivars. Sometimes in the world of horticulture, a cultivar, because of its good characteristics, is more popular than the straight species and dominates the world of horticulture to the point that the straight species is no longer sold.

The common name for many different species of Ligustrums is privet.

The world of horticulture is messy, on large account because we are talking about living things that can vary widely in size, shape and other characteristics, even if the same species. Plants don't stop growing so the numbers commonly listed for height and spread can vary quite a bit. They are guides, and often misleading since they state a size at a point in time, but not what a plant might become in later years.

Ligustrum/privet will work for you as it fits into the category of large shrubs that can be trained into trees. However, IME, it can become quite broad. It is a dark, heavy foliage mass and could probably come to shade much of your lawn between the house and fence.

While the species India hawthorn can become a small tree, most of those you'll find in retail sales will not get as large because the main use of this plant has been as foundation shrubs, where people want them to be smaller and they have been bred for that. You would need to be careful about what you buy in order to know that you are getting straight species or a large variety.

If I were looking for a solution, I would not rule out deciduous plants. While they don't screen completely during the winter, they filter the view enough that it is ghostly and seems less offensive. Then, of course, they give complete screening during the warm months when people are outdoors. They frequently have the benefit of spectacular floral displays at some point.

Ligustrum japonica recurvifolia is a very nice cultivar & makes an elegant small tree.