Avoid brisket entirely. Full “packer cut” briskets of the kind Hill Country makes are hard to get and almost impossible for home cooks to pull off. Instead, get some short ribs or flanken, as well-marbled as possible (the meat counter at a premium operation like Fairway or Citarella is best). For ribs, try to get untrimmed spare ribs, rather than the circumcised “St. Louis” cut. Hill Country's ribs are juicy and porky because all that extra bone acts as a heat sink and keeps the rib moist. Since you can't get Hill Country's links, which are made for them in Texas, the next best thing is Johnsonville Bratwurst, which are available everywhere. And for chicken, Bell and Evans is about the best you can do, though kosher brands like Empire and Murray's are also very fine. Get skin-on breasts and dark-meat (leg and thigh) quarters.
Apply a generous rub of kosher salt and coarse black pepper, of the kind that comes in a bottle in the cheap-spice aisle, to all the meats other than the links. In your grill, put two dozen charcoal briquettes on one side. If possible, get some oak or hickory chips, and soak them in water for an hour or so. A handful should be added to the coals every forty minutes. Once the coals are nice and hot, put the meat on the cool side. Then leave it alone. If you're looking, you aren't cooking! Adjust the top vents to about the halfway position, and cook the meat to the following times: short ribs and spare ribs (2-3 hours); brats (2 hours); chicken (90 minutes tops).
Pit to Plate
Here's how you'll know that your ersatz Texas barbecue is ready. The ribs, when lifted from the center, will flop but not break. The short rib will offer no resistance to a fork probe. The brats will be dark and look ready to blow up. And the chicken, when you pick up the “tomahawk” dark meat quarter, will feel as if the joint is moving cleanly between thigh and leg. You should be able to break it apart by hand if need be.
Now serve, with cold beer, and eat it right away. Barbecue cooks slow, but should be eaten fast. Happy Memorial Day!