I have some about the same size and was interested in the responses you'd get. Here's my two-cents worth.
First, adiquate lighting depends on what you plan to do. We do jumpers, so we need high, bright lights with uniform coverage that minimizes shadows. If we just used the arena at night for hacking, we could get away with much less. Decide what you want in front, 'cause it's not easy to change later and you can have safety issues with too little light. We used a lighting engineer / contractor to model ours.
Other than the sun, there is no cheap light on arenas. It will either cost you in up-front capital, in operating/maintenance cost, or in insurance claims....often all three. We used to have a show facility with large lighted arenas. When the lights went on, you could hear the electric meter break the sound barrier. There was the same amount of noise when I received the electric bill. Shows paid the electric bill and we quickly learned to limit the non-show night-time activity.
When we built this place, I put in plenty of power to the panel. The electric company is easy to work with on the initial install. Getting enough power from the pole is a major expense and it's even more expensive to try and increase it later.
I got a number of bids for lights. The best was around $20K. I could save about 35% by doing it myself. The expense is in the materials and equipment rental. In the end, we decided that the payback on the expense just wasn't there and we've operated just fine without them. With the material prices dropping, I'll probably look at this again in a few months.
My view is a commercial, risk-management one, so I tend over-engineer things like this. I have a friend with a dirt clearing and a dozen or so 150 watt light bulbs hanging over it. He rides at night and is very happy with his "lighted arena". It all depends on how you define it. What are you really looking for?