Use fishing tackle of various types. Worms will usually tell if there are panfish (bluegills and the like) pretty quick, hotdog or stink bait w/treble hook on the bottom for cat fish, minnow under a bobber or bass lures for bass. I like Rooster Tail and Mepps spinners.
You could also use a trap to see what comes in. I like to use a sock with some fishfood (dog/cat food works too) inside the trap,bread tied to the inside of the trap. This will tell you if you have forage type fish and, maybe, crawdads.
Some have had luck with throw nets...me, not so much.
Limb lines and trot lines are a more lazy approach. Not that there is anything wrong with that! lol
If there are fish in there and you stock small, affordable fish...they will likely become expensive food. If, by chance, you have decently balanced populations now, stocking may alter that in a negative way.
Using the above fish catching ideas may not produce much data until springtime. Wintertime tends to keep the fish much less active thus less hungry.
Your estimates are very high, indicating that they really don't want the work. I had my 1/4 acre pond renovated for less than $6K, IIRC and it was originally 10 foot deep, but had silted in with 8 foot of muck. It was a very old cattle pond. Of course, if you have to have the muck hauled off, that increases the costs a lot. If I recall, you suspected a leak too. That does not inspire most dirt guys. Your water depths would be healthy for a fishery I would think. So, you may be on the best course. Time to do some fishing.
Catch some between now and spring if you can. Measure their length and weights, keep track of the numbers and what species. Research "Relative Weights" of game fish and you can tell a fair amount about their health from that.
