What I usually do when I'm cutting pipe depends on how square it actually needs to be. If it's going to be bearing against a surface, or if I'm threading the end of it, flatness is very important.
If I can, I usually design things so that the ends of pipe don't need to be perfectly square, because that reduces work for everyone -- but sometimes it can't be avoided.
The general idea of cutting in from multiple parts of the edge is good. One good tip, if you want to be really precise, is to start the cut (without going through) at a few different places and slowly go in until you've got a decent groove in the material -- then you can start biting through the edge of the pipe and follow the groove that's already there (scribed lines and pencil marks can be hard to see and impossible to feel).
In order of increasing precision and effort, here are some ways to mark out such a cut:
Just start cutting from one point and go through to make a square cut (this requires pretty advanced skill to do properly)
You can mark a line and just trace it around the pipe freehand (quick but not very reliable) -- this requires some skill but not anywhere near as much
You can use one point, and then hope that you are able to wrap tape / scribe a line / etc at precisely 90 degrees to the pipe. This doesn't always work perfectly, but it will get you close
If you want it to be very precise, you can measure the distance from the other end of the pipe using a height gauge or a measuring tape or whatever) to two or three points around the cut. Then connect the lines using tape, or scribe them (or both!)
If you are obsessed with getting the cut perfectly flat, you can spray some layout fluid (Dykem, Prussian blue, etc) and then use a straightedge to scribe the line by rolling the pipe. This requires a non-trivial amount of setup, and is really not necessary unless you require an extremely close fit
When I am cutting anything with an angle grinder, I leave a good bit of space (maybe an eighth-inch to a quarter) between the cut and the final dimension -- the cutting wheel itself has a thickness, and it is not always easy to see small deviations while you're still in the cut.
Remember -- you can always go back afterwards and grind off more material from a part, but you can never go back and grind off less material -- unless you are a welder, but that is a different story ;)