OU DG rifles are just fine if you can find one, and they are inherently far easier to regulate or use with optical sights. I currently own two and several others have passed through the gun room over the years. There are just not many in the classic rimmed forties, because the Brits were able to define the dangerous game double in East Africa following the loss of Germany's colonies at the end of WWII.
A rimmed caliber is indeed best, though I regularly shoot a .375 H&H double that has never bobbled.
For that sort of money, I would look for a Continental double - Heym, Krieghoff, Blaser, Merkel, or Verney-Carron of recent manufacture. All five are far superior to a Sabatti. Most are probably going to be ok due to limited use.
There are lots of pre-war Birmingham made English boxlocks floating from hand-to-hand in your price range. In my experience, at least three-quarters will have some sort of issue (usually a very expensive issue) not readily apparent to an uneducated buyer. There are few bargains with double rifles and never any steals. Caveat emptor.
I personally would urge you to hunt your first buffalo with a rifle with which you are totally familiar and absolutely capable of precise accuracy. As a client picking a fight with a buffalo, your first and overriding responsibility is to put that first shot exactly where it needs to go - not close but exactly. Do it and everyone goes home to toast your kill. Screw that up, and you may get the opportunity to live with the responsibility of watching your PH or tracker be badly injured or worse. I have a dear friend who has been a PH in Zim and Moz for many years, and he always says that the one thing that truly terrifies him is a client on a first time buffalo hunt with his new double.
More practically, you will have to have the self-discipline to pass on a lot of opportunities. That is hard on our relatively short hunts these days - particularly a wilderness area hunt. Even at sixty yards trying to put a bullet through a tight window in the brush into the right spot on the right buffalo of a group of three standing together in the shade is a challenge with a bolt action equipped with superb optics - much less a double with salad plate accuracy at that range equipped with a big white bead.