This is a super old thread, so I am not sure any of the original posters will respond.
I will say that your arena can be simple and inexpensive, or you can spend (*waste*) tens of thousands of $ on footing and fencing and laser leveling and ...
You need to consider how much space you can devote to an arena, wether it can be *just* an arena, or if it can be multipurpose for grazing and riding. How often you will be riding, your budget, and your style of riding all come into play.
I competed every weekend, and took weekly lessons at my house, with a VERY particular classical dressage instructor. My arena? It was poly posts, screw on insulators, and surveyor's tape. In the middle of my pasture. I didn't need solid barriers, I just needed, and my horse needed, a visual indicator of the edges of the "space" we were riding in. I did not need footing. I had 10 acres of prime pasture, and only 3 horses, so I had plenty of space for a "real" arena, I just could not justify one.
As far as dimensions, you do not have to ride dressage to appreciate the value of a "dressage dimensioned" arena. Dressage dimensions are set in a particular way, to allow the horse to be balanced around the narrow ends. Google the dimensions, you can make it huge or tiny...
Round pens are also great, but smaller round pens SHOULD NOT be used for speed work. There is too much centrifugal force on the horse's joints, and it is VERY hard for a beginner rider to learn to have a balanced seat and balanced horse, when working in a small round pen. I do LOVE round pens, but they have their limitations.