You just need one circular needle to make your blanket. You just cast on like you would for straight knitting, and then when you get to the end of the row, you turn your work over and knit across again. I didn't see a video on this site, but there is one here:
(Don't worry so much about the stitch she is doing, just watch for how she turns the work around to knit the next row.)
36 inch is probably a good size if you want to make a regular afghan. I wouldn't get the size 15 though, because that is pretty big, and I think for most beginners, large needles can actually be kind of awkward. The 11s are fairly good sized too, but should be easier to handle.
If you do go with the size 11 needle, you should look for chunky weight yarn because worsted weight will be a bit on the thin size to use with those needles.
One more recommendation--when you buy your yarn, try to find something that looks fairly "smooth". I don't recommend you buy any really bumpy, fuzzy or novelty yarns, like Fun Fur, because they are a lot harder to work with and can be very frustrating for a new knitter. Heck, I've been knitting for awhile and they frustrate me!