The short answer
Since you are completely untrained, your first priority is developing strength.
Endurance is Bupkus Until You Are Strong
In the absence of developed strength, strength training always improves work capacity by reducing the relative intensity of repetitive tasks. (Mark Rippetoe, Starting Strength forums)
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.
