What is the correct right hand technique to play legato when only the first note on each string is picked? I am most comfortable with down picking whether I go up or down the scale, but as I learned over the years, not everything I am comfortable with is actually right way how to do it.
In this case I use downstrokes when moving up (towards the high E string), and upstrokes when moving down (towards the low E). This feels most natural to me. However, I'm convinced that there are (and shouldn't be) any rules as to what is right or wrong with such things. You should be open to try all possibilities to see what works best for you. It is true though that sometimes it takes some time to discover that something which initially doesn't feel totally natural becomes actually more efficient after having practiced it a bit. So, 'trying' everything doesn't mean to try it just once :)
Let me start off by covering the kinds of picking. As you mentioned, there is playing only down-strokes, called "downpicking". Mainly beginners do this, but some say it's also good to get a certain tone. Next, there's alternate picking -- which usually means playing a down-stroke followed by an up-stroke and maintaining that pattern for every note. Alternate picking is a mainstay, and chances are you'll always at least practice it (see: "speed-picking exercises").
After that, you have economy picking. In economy picking, you use down-strokes as long as you are descending, and up-strokes when you ascending. Alternate picking is then applied only when there is more than one note played on the same string in succession. You can also think of it as a cross between alternate picking and sweep picking.
Try economy picking, and if it doesn't feel right to you, then stick with what does. Beyond that, you'll need a good teacher to observe you closely and tell you whether you're doing it right. Usually, if there's a "correct" technique for guitar, it's to keep you from getting injured or putting undue stress on your body. Personally, I think that safety, efficiency, and comfort will all be found together.