Re diameter - that's a good size for the pen; boards or rails (however you go) on the inside is a good idea too.
Re height - I think you might be happier with more height - at least to 5 ft. For me, if I had to pick between more height and a solid wall, I'd go with height. My round pen, by the way, is a portable metal corral panel style one with a height between 5' and 5 1/2'.
Re footing - Grass probably isn't the best footing as it can be slippery especially at speeds. However, budget will play a part and you may have to live with grass for awhile and just use err on the side of safety in working the horse (that's where I'm at with mine). After it is used a few times, the ground will get beaten up and kill off most of the grass in the track. Eventually, it would be good to have your pen worked up and appropriate footing put in. I'm sure you've picked out a level spot with good drainage already - that will make it alot easier when you go to put your footing in.
Good luck - I'm sure you'll enjoy it when it's done.