I always use 3/4 for carcasses. Some commercial cabinets will go thinner, but with 3/4, you get better durability at the joints. For the effort you’re going to, the extra 1/4 inch or less you will save across the cabinet is nothing. You’ll end up with a more rugged carcass, and the joinery process will be a little more forgiving. Pocket screws, dados or Dominos in 1/2 stock require a lot more care. Cost and weight are little higher in 3/4" material, but the frustration will be lower.
Plus, you won’t want a 1/2 thick shelf. At 35 inches wide, there’s a good chance that it will sag. 3/4, with a 1/4 to 1/2 solid wood strip across the front edge will hold up well. Back panel can be thinner. Don’t get a second sheet of 3/4 oak ply just to complete the back panel.