Gunny, we are extremely fortunate to live in the Houston area. With a bit of care, you can easily feed raw for between $1.00 to $1.50/pound.
For the first month, definitely enjoy the inexpensive leg quarters. Watch for whole chickens to be on sale for $0.59/lb and that's when you'll give Gunner his white meat from chicken without costing yourself too much. And don't worry if you don't know how to cut up a whole chicken -- the dogs don't care whether they can recognize a particular piece of meat or not.
Once you're a little further along, there is a wholesaler (Action Meat) between the airport and Greenspoint Mall. You have to pay cash, you have to buy at least 100 lb at a time, and the items come in 30-40 lb cases, but many of Action's prices can't be beat, and they carry some meats you don't readily find at the grocery store: hearts from turkey, pork, and beef are all less than $1.00/lb, liver and kidney (pork, beef, chicken) will run you $1.09 or less, lamb breast ribs $1.99, pork riblets for $0.99, chicken paws/feet (great for treats and good for his joints) will run about$1.09...you get the idea. If you'll send me your email address in a PM, I'll forward a recent price list to you to look at.
When you're ready to start fish, Fiesta stores are a real jewel. You can find smelt and mackerel (both good sources of Omega-3s) for less than $2.00/lb and sometimes as low as $0.79/lb. And, of course, if you want to serve some shrimp (to yourself or to Gunny!), you can make the drive down to Seabrook and buy from the stores down there (underneath the bridge, on the north side). Shrimp season has started, so the prices should be $1.99 or so for shrimp that is perfectly fine for feeding Gunny.
The Asian Markets down off Bellaire (Beltway 8 south to Bellaire and turn left towards town) are a cheap source of duck. You can get hearts, feet, and wings for less than $1.00/lb usually, and the whole duck for about $1.69/lb. We've also found pork pancreas down there, which isn't easily found elsewhere. We recently scored 30 lb of pancreas for $0.50/lb.
And now that I've given you some great places to look for reasonable prices, I'll expect -- if you get lucky enough to score some deer meat this winter -- that you'll share that with me. hahahahaha
Be careful; sourcing meat for your dog becomes addictive and you'll end up needing a THIRD freezer.