I'm a programmer and I spend a lot of time sitting in front of a computer typing, and this seems to be too much strain for my back and upper hand muscles. All the orthopedists I talked to said these were muscle pains and that I should just start exercising (so this is not some injury, but rather poor fitness). However, I didn't think of asking them what kind of training that should be. Should I concentrate more on developing strength, or developing endurance? What are the pros and cons? Can I combine the two, and if so- what is the appropriate way to do that in a 3 times per week exercise schedule?
The short answer
Since you are completely untrained, your first priority is developing strength.
Endurance is Bupkus Until You Are Strong
If the muscle is weak, developing endurance is close to useless. That's because every effort for a weak muscle is a significant task. A stronger muscle barely notices those efforts because they are so minimal, and so endurance in relation to the task is much greater.
Develop a Baseline Level of Strength
A lot of people have success with Mark Rippetoe's Starting Strength program, because it is information-dense and builds whole-body strength rapidly. The program is essentially 3 days a week of lifting: barbell squats, deadlifts, overhead and bench press, plus chin-ups.
For the totally un-athletic, the exercises in Starting Strength may be a bit much. If that's the case, take a look at this great answer from Mike, particularly the part about lifting. Goblet squats and dumbbell deadlifts three times a week are a great recommendation for the totally untrained. (In your situation, I would add dumbbell overhead presses and assisted chin-ups.)
When to Move On
Once you have developed a reasonable amount of strength, it would be a good idea to work on endurance. The problem is developing proper strength goals for your situation. For instance, my pull-up goal ("15 in a row") is very different from my girlfriend's ("1 un-assisted"). You need to find some attainable medium-term strength goals that you can work on for a few months, so that you can then switch to a strength and endurance program.
For you, a good goal might be "able to squat with a barbell on your back that's as heavy as you are". It might be "five pull-ups". Once you reach it, you can think about developing a program that includes an endurance-specific component.
If you're a programmer that means you're sitting most of the time. This implicates that the muscles of your backline are overstretched constantly and the muscles of your front line are over tensed. This outs in an aching pain in the lower part of your back. Your orthopedists are right. You can fix this with exercise.
BUT And this is a great but.
Fixing this kind of problem is not easy. You should really talk to a good personal trainer. Conventional fitness exercises just don't cut it and can make your injury even worse. If you do the wrong exercises the situation of imbalanced tension between your frontal and back muscle chains will even get worse. I strongly recommend you NOT to do any conventional abs exercises like set-up, cruch, ... . This is an advice given by people who follow convenional wisdom. This will make your injury even worse! You should not do any intensive sports before your problem is fixed. If you really want to sport before your problem is fixed then I advice you to go for a swim.
You should do exercises that stretch/open your frontal muscle chains and relax your back muscle chains. That way the tension in your back will dissapear. It's hard to do this with conventional exercise so forget training on endurance, with weights, ...
A good personal trainer should know how to handle your problem. Once you start training you should already see improvement after a few trainings.