First of all, please don't make a dinky little useless one. Spend the money and make something at least 20mX60m, they are a lot easier to re-sell.
If you are in a cold or hot climate then insulation is nice to keep the heat in, or out. Make sure there are nice heavy duty industrial lights evenly spaced and also if you're in a cold place find the heater that's right for you. Windows are also a nice touch. And make sure you have sturdy kick boards! You really don't want a horse kicking out and going through the wall. A storage/viewing area is also a nice touch if you don't want to be crowding your arena corners. And mirrors are also a bonus.
For the footing, make sure you are on solid, level ground. Put in a good base of road crush/clay and pack it down like nothing else. Then top it with good quality sand, too fine and it packs, too coarse and the footing will be too deep. Then you can add stuff, like rubber for "spring", shavings to hold moisture or the newest, coolest thing, felt. Felt is AWESOME. I love riding on felt. It is expensive though.
Don't cut corners when you are building it beause believe me it costs a lot more to redo the base of an arena instead of doing it right the first time.
Get opinions from local people in your area too because soil/environmental contitions vary from region to region.