Welcome Slick, I'm sure you'll enjoy SCI this year and have an amazing time on your first Safari. Get ready to be bit by the bug. Pay attention here, Gun Broker, or Guns International and you'll find a .375 H&H in no time. You'd be surprised how many gun stores have one sitting on the shelf somewhere.
I've personally hunted with 4 different outfitters in Africa. 3 in South Africa and 1 in Namibia. I've got plans to hunt with another outfitter in South Africa this coming summer along with several friends who've never been to Africa. Of my hunts, 2 started at SCI or DSC as Auction Hunts. The other 2 hunts (both RSA) were tacked after learning of offers by some of the AH Sponsors and were for specific animals. This has given me a diverse perspective on different operations (not as experienced as a lot of individuals on here though). Going forward, any hunt in Africa will likely come from speaking with specific outfitters at DSC/SCI, or word of mouth referrals since I now want to start targeting specific species where they're endemic. For a first time Plains Game Hunt, I don't think you can really go wrong. Below are some questions I'd ask
1) Pick an Outfitter/PH who offers the species you want or has access to places that offer them - Depending on the length of your hunt, I suggest 2-4 main targets, and 2-4 B-List Species you want to target if opportunity/time presents.
2) Ask how large of an area you'll hunt - Some smaller places hunt like they're much larger and vice versa, but 3,000 acres can only hunt so large and hold so much game.
3) Ask about a naturally sustaining population where you're hunting - Not everywhere has this and there are a lot of places with put and take hunting on specific species. I'm not knocking this), but if you're considering buffalo, this will be important. This also ties back into the size of the place.
4) If you bow hunt or want to, make sure you speak to the outfitters to ensure they're knowledgeable about bowhunting and don't just offer blinds over waterholes.
5) Ask if you'll be in camp alone or with another group - I've hunted both ways and don't mind one or the other, but some prefer to be the only hunters in camp.
6) Ask if you'll be hunting with them or a different PH. If another PH, ask how long they've worked for the outfitter and their experience.
7) Ask about loaner rifles if you're unsure about bringing your own - if you plan to bring your own ask if they do the paperwork or have you use a 3rd Party.
8) If your bringing any guests or family, see what other side tours or attractions they can accommodate.
9) Amenities - not huge for me, but everyone is different and if bringing guests you might want something a little less spartan.
10) Ask about references - some outfitters cater more to American clients and others to European, or South American clients. This will impact how they hunt, and their amenities mainly, along with pricing.