I fish a lake similar to what you describe and would suggest the following;
1. Use a pendant lead on a run ring. The lead will often plug into the clay which, if you are using an inline, could hinder presentation.
2. The water in clay dug pits is often quite murky so you don't need to worry too much about camouflaging your end tackle. My starting approach would be a supple braid link of anywhere between 8-12 inches with a line aligner and balanced bait or a bottom bait straight out of the bag. I don't fish popups on this lake as I think one of the main benefits of a popup is its visual nature and in murky water, that benefit is lost. In terms of the rig, I find the supple braid presents much better over this kind of substrate than a stiffer material.
3. In terms of bait, scent is more important than the visual aspect, again due to water clarity and the fish needing to find the bait via smell rather than sight. I use a dark, fishy, L030 based bait which works really well and kicks out loads of smell although I have also had plenty of success with a Mackerel bait and Krill based baits too. I assume any decent fishmeal based food bait would do the trick.
4. Stealth and watercraft will be massive assets on waters like this (in fact any waters really) but on a small water, do the basics right. Things like keeping your shadow off the water, treading lightly, not thrashing the water to a foam with the marker etc can definitely win you more bites. I also find that light scatterings of bait or just a bag or stick in the right place may be a better approach than piling the bait in unless the fish are really having it.
5. Pay attention to the weather. Small, clay dug pits are often shallow and you will most likely find the fish on the end of a warm wind (or sheltering from a cold one).
6. Most importantly, find the fish first. As the old adage goes, 'you can only catch what is in front of you'. If you can, have a few laps of the lake before setting up and try and spot some fish. If it is a club lake rather than day ticket, go for a walk around it of an evening after work or at first light and start piecing together the puzzle based on sightings. You can even stack the odds in your favour by taking a pocket full of bait with you and dropping a bit of bait into some likely looking areas. Every time you come back to the lake, have a look at the baited spots to see if anything has visited. This approach of little and often pre-baiting has really upped my catch rate on my lake.
I hope that helps
Tight lines