As a homeowner with trees, it is in your best interest to take good care of them. I am not suggesting you buy some expensive equipment or take a tree climbing class. And you don't need to take a correspondence course in Botany; actually, the Botany you learned in high school will be more than sufficient: the basics of photosynthesis, some idea of liquid transport, how they move water and nutrients upward inside the trunk. Perhaps I am getting carried away…
What is important is your connection with trees—how you sense that as they get bigger they will need more water. How you know that halfway into a hot, dry year they need a long drink. The number one most important action to ensure your tree’s long and healthy life is how you water them. I can’t do this for you. The knowledge and experience of an arborist can be a life saver, but only you can water them. And if you do, and you give your watering program some thought, you’ll find that the arborist doesn't have to come by all that often. Your well-watered trees will pretty much take care of themselves.
After a few years, you will get some inside deadwood. That's natural. As the tree continues to grow, it shades itself. The shadiest inside area of a tree’s crown is where you will find that deadwood. As for diseases and insects, if your trees get the water they want, you will see very little of either. Both the bugs and the disease will be on the thirsty, struggling trees down the street. That is not to say that you won’t get visits from time to time; a lot of different caterpillars pass through, though usually they don't stay and do much damage. I don't mind buying them lunch, but if they move in for a fortnight that’s a different story!
The other practice of great importance is your visual inspection of your trees. During the growing season, walk around and through them. Once a week gets full marks. By now you have got to know them well and any oddity will stand out. It is this level of attention that catches a disease just as it starts, and makes dealing with it easy for you and the tree.
The other extreme is a nasty condition that doesn’t get noticed until a major section of the tree is dying and has to be removed. This is most likely the tree that never gets watered.
Take your pick—pay for water or pay for tree removal. One last idea: trees know what they are doing. Seriously, a hands-off approach will get you a lot further than over-pruning, and over-fertilizing. A healthy tree in the right spot, maturing into a beauty, is a joy for the world to behold. Enjoy.