I’ve been giving this question some though this afternoon, and I think I need to expand on my last post. Simply saying I’d only purchase the Yamaha from that list doesn’t really explain anything.
Let’s start with the C# Trill Key, I doubt very much that you’ll find a decent flute with this option, within your budget. Even second-hand. Think of this key more as a specialised key. It lends itself more to those that primarily play in orchestras. Can you play in an orchestra without one? Yes, you can. I did for over five years. Soloists on the other hand, I’ve found tend to play flats rather than sharps. This of course is a generalisation. I suppose my point is, that you don’t need one at this point in you flute career, as it’s an unnecessary expense.
I would recommend getting a flute with an off-set G key, and a split E mechanism. I wouldn’t worry too much whether the flute comes with a C foot or B foot. In the early days, a C foot can be much easier to play, and many continue into their professional careers without a B foot. I won’t get into a closed hole vs open holes debate here, but if you do opt for an open hole flute, I suggest you just rip those plugs out and get on with it.
As for Gemeinhardt, personally I’d steer clear of that brand.
In my opinion a student Yamaha would be a much better option for you. Any Yamaha YFL-2**, YFL-3**, YFL-4**, YFL-5**, etcetera would all serve you well at this stage. Even the second-hand Yamaha 584 HCT you mention would be a good choice, that you can grow with, just as long as it has been serviced and is playing well.
The most important thing to remember is that good technique, embouchure, and dedication to your practice, far outweighs, what flute you play / own / purchase.