Trees in the Prunus genus (cherries, plums, peaches, nectarines, etc) can produce some awesome tasting fruit, but keep in mind that they are relatively short-lived trees that are very prone to disease and insect damage. If you choose to grow fruit from this genus, just be aware that the trees are more temporary than most other types of fruit trees. You can decrease the severity of the problems (at least temporarily) with diligent spraying regimes. Many home growers end up not keeping up with the required maintenance and wondering why their trees become sick and die at such an early age.

Pears are pretty tough. Fireblight is probably the major problem that you'll have to deal with. You may want to consider cultivars that are resistant to, or tolerant of, fireblight.

Apple trees can be very long-lived, but are probably the highest maintenance type of fruit tree of all fruit trees. The four major apple diseases (apple scab, fireblight, cedar apple rust, and powdery mildew), as well as multiple pests, make spraying pretty much a necessity when it comes to these trees. Even if you choose cultivars with good broad-spectrum disease resistance (and only a hand-full of cultivars meet this criterion), you'll still have to spray for pests. Choosing the best varieties (of scion AND rootstock) require careful evaluation of your goals and desires. There are no perfect perfect scion or rootstock cultivars; all have pluses and minuses. You'll need to figure out which pluses and which minuses (taste, production, storage potential, preciosity, disease resistance, growth rate, amount and complexity of maintenance, ease of pruning and harvesting, drought resistance, anchorage, adaptability to your soil and site conditions, etc, etc) are important to you and for your application. I can cover this more if you have further interest.

Many other types of fruit trees are available, and I would encourage you to look at other possibility as well as the ones you have mentioned. Pawpaws, native persimmons, and maybe even some types of figs are examples of some easy-to-grow, no-hassle types of fruit trees. Each has special considerations that should be considered, but they are all pretty simple. If you are interested in any of these, or other types of fruit, maybe we could cover the specifics of what you are interested in.

As for your black walnut, you may not have to worry about it too much longer. I don't know how soon thousand cankers disease will make it to Nashville, but my guess is that it won't be long. New reports are occurring more broadly and frequently. I hate the thought of loosing my black walnuts, but I figure I have only a few years (at most) left to enjoy them (baring some unexpected advance in fighting that serious disease).

Choosing your trees very carefully (including rootstock), planing your trees properly (very, very, very important), and understanding their maintenance needs can go a very long way towards maximizing your results and your enjoyment of fruit trees. Below is a guide to help you with planting procedures. If you have ANY questions about any of the points, PLEASE feel free to ask. Really good planting guides are hard to come by. Many have errors or leave out very important points. A year or so ago, I wrote the instructions you'll see in the link with the help and input from many of the regulars on the Trees Forum. If you do see anything you don't understand or have questions about, it could be helpful to me (as well as to yourself) if you'll ask. I am still in the process of fine-tuning the instructions. One day I'm going to get around to adding some graphics.

Here is a link that might be useful: Planting a Tree or Shrub

Wow, so much information to consider! Thank you.

How long is short-lived when it comes to fruit trees?

Since I'm new to fruit trees (and growing things in general), what lower maintenance trees would you suggest? Would especially be interested in self pollinating varieties. I'm now considering pear, nectarine, cherry, or fig -- mainly because I like those fruits, and can see actively making use of those fruits. My dad suggests pawpaw, but I have no idea what you do with pawpaw. What does it taste like?

I had thought apple, but then I read up on them and realized growing them may be more involved than I'm willing to do at this point. Also, I read there are potential problems with planting apples near black walnuts because of juglone from the roots. What other plants should I avoid around my black walnut?

Also, any suggestions on where to buy the trees? Although I have a few places in mind, recommendations for reputable nurseries are welcome -- I'm in Nashville.

Average life expectancies vary greatly between different types of fruit trees and with a number of factors such as rootstock, climate, planting methods, maintenance (pruning, spraying, etc), various site-related factors, etc. One of the shortest lived types of fruit trees is the sweet cherry, and the typical life-span for those is probably 10 to 20 years. Sour/pie cherries are a little better, but are still short-lived compared to other types of trees. Apple trees, for contrast, can live well over a hundred years, at least if grown on a full-sized rootstock (there can be disadvantages to full-sized rootstocks, BTW) and grown in reasonably favorable conditions.

Choosing specific cultivars is usually something you do after choosing which characteristics are important to you, what your planting site and situation requires, and which cultivars you like the taste of (at least if you are growing the fruit to eat). When it comes to apples, pears, and cherries, at least, one needs to narrow down the specifics before they can really pick a cultivar. Even most other types of fruit trees require consideration of multiple factors. There are almost too many characteristics and considerations to cover them all completely here, but examples of some of the primary things to consider are:
1.) Is taste, disease resistance, or one of the other many factor most important to you?
a.) If taste is most important, which cultivars do you personally prefer?
b.) If disease resistance is most important, are you willing to spray some or would you rather have "no-spray" (at least so far as disease goes) cultivars?
c.) If some other factors are most important, you'll need to evaluate appropriately.
2.) What is your site like?
a.) amount of space available per tree
b.) sun exposure
c.) wind exposure
d.) soil type
e.) drainage
f.) climate
g.) availability of supplemental water
h.) etc., etc., etc.
3.) At least in the case of apples, is life expectancy, precociousness, or ease of pruning/spraying/harvesting more important to you?
a.) If life expectancy is of primary concern, you might lean towards a semi-dwarfing (or possibly even a full-sized) rootstock.
b.) If precociousness or ease of pruning/spraying/harvesting is more important, you might want to lean towards a dwarfing rootstock or maybe one of the smaller semi-dwarfing types.
c.) Are you willing to support the tree until it is established? permanently? If not, an appropriate rootstock for this factor must be chosen.
4.) For plants like figs, are you willing to store the trees in a protected area (an unheated garage, for instance) or do you want something you can plant outside and leave?

We could cover specific types of fruit trees, one at a time in separate threads, but it's probably just too much for one thread and for a short period of time. Sometimes I hate to even recommend the Fruit and Orchards Forum (it can get annoying and expertise varies greatly), but that's probably the best place to start getting a feel for what you need to look at.

Here are examples of some of the cultivars I grow in my home orchard (not at my home, but that's another story), but don't assume these are the best selections for your situation, necessarily. What was important for me (mostly low maintenance even at the expense of taste in some instances), may not be what is important for you and your situation.
Apples: Freedom, Liberty, Arkansas Black, Virginia Beauty, etc. all on EMLA111 semi-dwarfing rootstock
European pears: Magness, Moonglow, Potomac, Seckel, etc. on OHF87, Betulifolia, and OHF333 rootstock.
Sweet Cherries: Black Gold, Black York, and Regina, etc. on Mahaleb and Mazzard rootstock
Sour Cherries: Montmorency, Northstar, Surefire, etc. on Mahaleb and Mazzard rootstock
Native Persimmons: Early Golden, Loverboy, and Morris Burton
Figs: Brown Turkey, Celeste, Chicago Hardy, UCR143-36, etc.
Pawpaws: NC-1, Overleese, Shenandoah, Susquehanna, etc., etc.

There are a few types of plants that are tolerant (to various degrees) of juglone, but I would basically assume that all plants could be affected, because most can be. There's nothing unique about apples, in this respect.

Where to buy? I'm glad you asked. Stay away from the big-box stores, approach local nurseries with skepticism, avoid the suppliers at the bottom of my attached list (the ones with poorer reviews) like the plaque, but check out the many great choices on the following list:

Here is a link that might be useful: Sources for Fruit Trees and Plants