Depending on hair / outfit, I tend to go for jewelled hair clip.
I went to an event at the palace last summer and there were more hats than fascinators, but I don't know if that translates to weddings.
Agree with Liz though. It's about the outfit as a whole and I do think you height and build comes into it (for example, I am short but relatively broad of shoulder, so I tend to avoid both the very flat brimmed hats, but also anything terribly delicate). Plus there is truth about what you feel confident in. It doesn't always translate to feel fab == look fab, but one thing is for sure, if you feel awkward, you'll look awkward.
As to milliners etc. depends what you want to spend. I don't get much opportunity to wear hats so I pitched up at the palace last summer wearing a hat my mother lent me, that I think came from House of Fraser or John Lewis. YMMV. I didn't mind pitching up for a £££ dress and already had the shoes, but just could not justify hundreds for a hat.
Plus at a wedding if there all day, you will more than likely take it off, if not for the meal, certainly for the dancing. For that reasons alone, Cherry Chau or Swarovski clip?