What a debate. IMHO, I would suggest learning the major and minor patterns first (along with the notes on the E and A strings). I say these first because they are the foundation of everything else (how do you explan that a Dorian mode starts on the second of the major scale if someone doesn't know the major scale?). Then, as an introduction to the modes, point out that the minor is the same thing as an Aeolian mode, which starts on the sixth. I think it's important for beginners to realize that these modes exist, that there is more to music than major/minor. However, using them properly will probably take some time. But why not give beginners the information and let them incorporate it as they mature. Also, in my experience, I only think about modes when I'm writing a piece of music. If I'm trying to learn a cover song, I general just try to figure out the key and listen for the intervals. How much someone will use modes depends on how much they want to study composition.
Like many things, I'm not sure there is just one answer. It really depends on the student. If you have a student that struggles through a one-octave major scale, they are probably note ready to learn modes. Again, how do you explain them? If you have another student that can rip through scales as fast as you can call them out, then they are probably ready. However, the theory and use may take a while to develop.
Another point about modes and AB, if you try to use the "Scale Finder", you have to know at least the names of the modes. There isn't a major or minor scale list, only an Ionian (major) and Aeolian (natural minor).
Anyway, back to the original question as to scales for a beginner to learn, start with the patterns for major and minor scales AND memorize the notes on the E and A string. The basic pattern for major and minor in the key of G (one sharp on F) are:
Hope this helps!