Yes - mark the corners first. You probably want to make use of whatever you happen to have around at the time. You won't really be using the corner markers after you've got going, because you'll wear a track in the field, and you'll be using your letter markers for accuracy. A short-term corner marker solution might be to paint some rocks white, for example, if you have rocks in the field anyway. I'm a bit wary of drainpipe or any other rolly thing that can be a hazard if stood on (and things that are going to have to be removed as trash at some stage).
The only thing that's really tricky is to get the corner angles right. It is really easy to make a parallelogram, rather than a rectangle. Well, strictly speaking, you WILL mark out a parallelogram, you just want it as close to a rectangle as possible. You need to use a bit of pythagoras to get your angles right. You remember the famous 3-4-5 triangle ? Any triangle with the lengths in the ration 3:4:5 will contain a right angle, so make one out of string. 3m, 4m, 5m works well - tie a loop exactly 12m long and mark it at 3m, 4m, and 5m. When you come to stake it out, you will have an exact right angle to put in your corner, and working form there, you can stake out your line to the next corner. When you've worked your way round all four corners, you'll be out by a little way but far less than youwould have been if you just do it by eye.
In fact that would be a neat experiment - mark out a 20 x 40 arena using a tape measure, but guessing at the angles, and then measure the two diagonals. They should both be the same - 44m 72cm - but I'd bet they'd be a long way from that.
