I have about 3/4 acre pond, max depth 10', which we drained to 3 feet and renovated the banks this past spring. I posted an earlier question about foul smelling bottom mud, and the recommendation was to aerate. There is about 18" of this grey mud over most of the bottom; the ponds was surrounded by trees and brush up to the water's edge prior to clearing this past spring. There was also runoff from a 3 acre field planted in hay, which we converted to pines two years ago. Since I have significantly (I hope) reduced the amount of organic debris entering the pond, how should I aerate? I assume a disc membrane is best, but do I immediately place it in the middle of the pond, on the bottom, or should it be suspended above the mud layer? Also, what are the benefits / problems with de-stratifying the thermal layer? We recently had heavy rains and the top 12" are much warmer than the bottom layer. Prior to that the pond had not filled from the drawdown and the entire water column was probably 80F +. I honestly have no idea about the fish population, but we do have a lot of turtles and frogs, so I'm guessing that there aren't a lot of bass.

First, search this site. There are volumes of thoughts that go directly to the heart of your question.
Directly, here's some answers. There are a number of excellent companies who can assist your decision which aeration system to buy. Look at our resource guide, and if you aren't a subscriber to the magazine, call the office tomorrow and ask Kathy to send you a copy of the magazine. Subscribe to the magazine. Inside, you will find several advertisers willing to step in and help.
Destratifying the lower layers is an excellent management decision. Mixing water layers helps cleanse the entire pond, if done properly.
Third, I would figure out the status of your fish population. Depending how long your pond was down, your fish population may have made major adjustments. Now that it's full, you may need to adjust it yourself.