Definitely baseboard first. You can mark where the studs are on the concrete for a solid install of base. Use a piece of 3/8" thick trim as your 'guide' or shim for the height of the base off of the floor. Depending on the floor, you may find that the concrete is wavy and the gaps left will be + - the 3/8". The tack strip and the carpet are the only components that are up to wall. Carpet pad thickness is irrelevant. The 3/8" gap will allow carpet installers to tuck carpet under base for the best look, as long as you are having a plush or 'frieze' carpet installed. IF you are using a thinner carpet like a commercial carpet, you will want to keep an eye on that gap so that it doesn't exceed the height of the carpet on a piece of tackstrip (or if it is being glued down). This will look bad.
As far as mitering vs coping goes, I hate coping, so I always pre-cut some scraps of base to see how the corners look with a perfect 45' cut, and then adjust miter for precise cut. If you do want to use coping method, cut one board square and tight to corner, then cut next board at 45' cut, and use coping saw to follow the line of where the 45' cut starts, right to the top tip of mitered cut. That make sense?