The default is grey, just be sure to customize your magic bands online as soon as you book your stay and yes they will be shipped out immediately by 2-day delivery for short booking windows (Based on my experience earlier this month). I've never picked up the magic bands at the resort, but I'd think as long as you customize your color online you'll get that color at the resort, but if you don't customize ahead of time, the default is grey so that is what you get.
And yes you get a magic band for each reservation. I am actually annoyed with this, I often go for short stays as an annual passholder to catch different special events like 24-hours, harambe nights, villains unleashed, Christmas, etc. Now I have every color and am starting on duplicate colors!
Oh and all the magic bands are interchangeable for each person. So you can use whichever one you want for either resort stay. It isn't linked to a particular reservation just to you as an individual and the computer will know all the reservations, park tickets and fastpasses under your name. You can monitor all this online in My Disney Experience to make sure the computer has it all correct for you and your family.