I play both flute and oboe and despite that most of the people says that plying the oboe destroys the flute embouchure, I haven´t have any problem with combining flute and oboe.
I belive that the hardness of the reed one shold use is quite invidual. Harder reed -> higher pressure, less volume, Softer reed -> less pressure, larger volume, so it depends of the size of your lungs, your diaphragm and more.
Since it is easy to be accustomed to a wrong type of reed, I always try to do mine so that I can play with maximum dynamic.

I assume you are referring to factory-made reeds. Emerald reeds in general are well-made and consistently good, but I haven't actually heard of most of the other companies you mentioned. Until you learn to make your own, I would suggest buying reeds online: what costs $20 at my local music store costs just $5 online. I would stay away from Jones reeds, as (according to my experience, at least) they are often inconsistent and in general are badly made.

As for the hardness of the reeds, you need to figure that out yourself by trying some out. Unlike on clarinet, one doesn't move up levels of reed strength as one plays better, so it really depends on where you are now. As a flute player as well, I started out on medium strength reeds and still use them to this day. If you start out on a reed that is too hard, you will have trouble playing for even short periods of time, your lips will probably ache (if you're just starting out) and you may develop habits, like pinching, that will be hard to remove later.

My flute playing has helped a lot. It lets me control my air and taper notes better. Besides, a knowledge of the fingerings and tendencies of flute will help a lot with oboe.

Good luck.

Do NOT start on hard or medium hard reeds! If you're buying factory reeds, use medium or medium soft. If you start on a reed that is too hard for you, you will have to pinch (use pressure from your teeth) to control the reed instead of just using your lips. This is a very bad habit to get into. If you're going to use store-bought reeds, I would recommend playing on a medium-soft for the first few weeks to let you build up some muscle before moving to a medium. You will probably not need to play anything harder than a medium; harder is NOT better in oboe reeds. Attempting to start on a hard reed (which is likely to be far harder than any professional would play on) won't improve your endurance, it will ingrain some really bad habits with your embouchure.

Also, store-bought reeds are really low-quality. Oboe reeds are supposed to be hand-made, preferably by an actual oboist. I don't think it's possible to mass-produce oboe reeds at that quantity and still have them be good. It's okay to start on a store-bought reed while you're just learning the basics of how to play, though they tend to have pretty frightening tone, but you should move on to something better pretty quickly. Is there a college with a decent music program anywhere near you? Usually you can get a college oboist to make some student reeds for you. Those should be good for a while. Eventually, it would be a good idea to move on to hand-made professional reeds, which can be found online. I recommend Rebecca Collins' reeds (http://www.oxfordreeds.com/reeds.shtml).

You also might want to consider getting a reed case. Try this site: http://www.forrestsmusic.com/oboe_reed_cases.htm. The protec 8-reed case seems to be the best deal at the moment. Actually, the same case seems to be a whole lot cheaper on e-bay (http://www.ebay.com/itm/Protec-Oboe-Reed-Case-Black-Holds-8-/300666965521?pt=LH_DefaultDomain_0&hash=item460125ce11).

Are you going to have an oboe teacher? I would definitely recommend taking private lessons, especially on oboe.

<Added>

The oxford reeds link only works if you delete the parenthesis at the end. Oops.

I have successfully played both instruments without experiencing any embouchure problems, and almost every other flautist-oboist I know says the same. In what way was your flute embouchure destroyed? If your flute tone sounds unfocused, try not to pinch down on your reed as much. Also, I believe dynamic exercises on both instruments will let you control your air speed more effectively and let you switch between instruments more easily. However, to understand your problem, you'll have to be a bit more specific.