What type of brush should I buy to prevent as much shedding as possible?

Depending on whether your Beagle has an undercoat (ask your vet), I've heard great things about the Furminator. If he doesn't, then shedding shouldn't be too big of a concern.

What type of doggy treats should I get to help me train him more easily?

Honestly, Beagles are known to be so food motivated that the healthiest treat you can use is his daily amount of kibble. In the morning, serve his food for the day into a container and use it throughout the day for training in order to reward as much good behavior as possible without the concern of overfeeding. For high-value treats for the harder stuff, my pups can't stop raving about freeze dried liver

What brand of dog food should I get for him?

Brands that are typically well regarded include Orijen, Acana, Taste of the Wild, or Merrick to list a few. Personally, I feed Orijen, but Acana is also a good option if you are on more of a budget or your dog requires a lower caloric density.

Best of luck with your new puppy, and feel free to ask if you have any more questions!