How much water flow do we need to keep the water aerated enough to have fish?

We have a big 70,000 gallon pond with a liner.  (I know, liner isn't appropriate technology IMHO, but I'm just trying to help us do the best we can with what already exists.)

The people who installed it originally didn't finish it, so it has a skimmer set up at one end but no pump running, so the water is basically stagnant right now.  I want to get something running so it doesn't turn into something nasty this summer.  We intend to have a pump run off our existing solar panels during the day, that will pump water through the skimmer/filter and then have it flow back into the pond from above at the far end, through some kind of aeration system, i.e. a lot of rocks.  What I don't know is, how big a pump do we need/want?  

Some details:
- The skimmer is rated to handle a 15,000 gph flow.
- I estimate the pond surface area at about 2000 sqft.
- The pond is in forest, so it's half shaded most of the day, probably gets about 5 hours of full sun on average in mid summer.

 I've read some places saying you want pond water to be cycled every two hours, which is not going to be possible here.  Even with a 15,000 gph pump, supposing we can run it off solar for 7 hours a day, that would cycle it 1.5 times a day when the sun is shining.  ((15k * 7) / 70k).  But we'd rather not use such a huge pump if possible.  

We don't need the water to be completely clean, but we do want to be able to have fish in there and not have a horrible mosquito hatchery.

How should we decide how big a pump to get?  Our current solar setup to run it off is max 1800W.

A pond liner is fine, if it's necessary. In my case it absolutely was. As for not having a mosquito mess, you don't need artificial circulation necessarily for enough fish to eat mosquitoes. How many fish your pond will hold is relative to the surface area, which is where the air exchange happens. You also have to factor in the affect of a cloudy week following a sunny week here, which can result in oxygen deprivation below the surface. I use feeder goldfish because they are the cheapest edible fish I could find in my area. I have 15 in about 25 sqft of surface area. I also plan on getting my pump set-up, but that's because I want to up my numbers in order to have a sizable harvest by increasing the air exchange rate (and because its cool). Your pond sounds big enough to eat comfortably out of as is, IMHO. Good luck!