On Ravelry, I found a pattern for a very simple cabled hat that used bulky weight yarn and big needles. You can get the pattern for free here.
The pattern says to use size 13 needles but I didn't have those, so I just used size 15 and made the smallest size. However, last night at a quarter to midnight when I tried the hat on (I was on the last couple of rounds by then) I found that it was far too short.
So, this morning I ripped all the decreases out and did another repeat of the pattern, and then finished it up. It's still a little bit short, but only by a few millimeters, and it's very comfortable.
As I knit it, I wasn't actually thinking about it being my first hat and it wasn't intimidating at all, which was good. I just did what the pattern said and tried to avoid making any alterations to the pattern. I succeeded pretty well I think, and didn't make any mistakes but at the end I had 8 stitches instead of only 6. I can't see anything the would suggest I messed up.
As this hat only took a total of 3 hours or so, I will definitely be looking at more bulky weight hat patterns. Maybe for the next one I'll even get the gauge right!