Get a 3 panel slider, and for that large opening I'd highly suggest a well-built and airtight door . Okna and softlite have the best air leakage ratings that I've seen. I'd imagine that you should be able to come in under those prices with a reputable dealer.
Hinged doors would be more. Stay away from box stores if you can. They seem to be hit or miss on installs, and lack knowledge if you are going DIY.

+1

If you don't mind the slider, they make a great unit and can usually be had much more cost effectively than swing doors.

For something as complex as a large patio door install, i would NOT recommend doing it yourself. Pay a little extra and have a pro do it correctly.
I agree with " karate guy", invest in a quality door, dont look for a cheap price, it will prove to be a very expensive mistake.

+1 to all of the advice above. Good product recommendations and I'd concur with cost savings on sliders as well as a professional installation unless you are very experienced in carpentry and have all of the proper tools and equipment.

To be clear, I am not doing the work myself. I am working with a contractor I have used before who is a great craftsman, but my arrangement with him means I source, plan and pay for stuff like this, and he installs it at a very reasonable price. This means I have to do the research on the products, but I kind of like that :-)

I don't really understand pricing on windows and doors. In a previous remodel, I bought three sets of French doors at HomeDepot, Atrium Pro line, the epitome of a big box buy. They are wood with aluminum cladding, grills inside and out, pre-hung with effective weather stripping (at least effective enough for our mild NorCal climate). After six years, they have never been painted and still look great. They cost about $700 each. I love them and would definitely use them again, but Home Depot no longer carries them.

Anybody have experience with imported mahogany doors like this: http://www.buywooddoors.com/shop/product/21

I have had something similar on the main house for about three years and it is performing well. I painted it out white, so I expect more maintenance over the long run than with the Atrium doors, but this is looking like it might be my most economical option.

The stuff that you are talking about is pretty low end. You won't find any professionals recommending it unless you use the term "professional" VERY loosely. You may be able to get away with it for a while due to the mild climate (as it sounds like you have so far), but you are really asking for problems at some point. A high quality single door will cost more than that at a wholesale price, let alone a double door, or the opening in question with potentially 4 panels.