I use lightweight tubes and size them smaller than recommended. Given that two are in use and there are usually two spares, the difference in weight is fairly substantial. They also are easier to mount.
I don't carry a spare tire. I've never had a tire I couldn't repair well enough to make it to somewhere that a replacement was available, but if that ever happens I'll hitch a ride.
I have used a variety of pumps including the Topeak Mountain Morph and a variety of mini pumps. Balance the weight against the convenience and pick one that suits you. These days I lean toward lighter as better. When I was topping off tires on three bikes on the Trans America I was happy to have the bigger heavier Mountain Morph. When I was traveling ultra light on the Southern Tier and in the Colorado Rockies I was glad to have an ultralight mini pump.