What I would do is look for an Oriental (10 x 12?) with a bit (at least) of the blue in it, as well as brownish and red shades (there are loads like that) and then (seeing as you didn't ask :-) I wouldn't replace the beige set with another chair, but put a big parlor palm or something similar there. You have the makings of a great traditional space (so glad the beige is going) and I think a plant and the right rug would just finish it off perfectly.

I should have mentioned, the chairs and curtains that look blue are actually green.

I'm all for asking what others would do, but you have to live with it. As to how big a rug and where to put it - while you're deciding on that, lay out newspaper where you think you might like a rug both at the end of the room or covering the larger area. That will at least give you an idea of the size to look for and help you decide if the rug will stand alone or be partially covered by furniture, etc.

And most places selling carpets will let you try them out in your home - a "seven days to love it" type policy. With browns, greens, tans - the burgundy carpeting can even become a neutral - there are a bazillion rugs to choose from and it's narrowing down the choices that is definitely the hardest. And in many cases, what might appear to be a mistake is simply getting used to something new.