Well, my first thought since most of my family lives in Louisiana, is what part of the state do you live in..??? Do you have enough land so you won't 'offend' the neighbors, when you 'do' what you want to 'do'...???
If I had a chance to do somethin' like this, I'd start with a 'shallow' end, and then dig as deep as I could , maybe 'waist' deep...??? Or even deeper if you could....... It was always a lot of 'fun', back in the old 'G.G's' days, to just start off gettin' just a little bit muddy,, knowin' that eventually, you'd end up in the big, deep mud-pit.....
Whatever you do, watch out for the snakes, the 'gators', and the 'crocs'......
For over 250 years man made waterways have been lined with clay. Around here that is Blue Lias clay which is extremely impervious to water. You would have investigate your local sources for the correct grade available. The advantages of clay is that it is easily repairable should something sharp go through it (almost self repairing) and you don't need to empty the thing to carry out any repair, just 'puddle' it (ie. stamp your foot on the effective area.) It will also last a long time (250 years?)
A modern equivalent is a modern pond liner, but if it gets punctured, watch out..As to depth you don't need it deep enough to drown in. A couple of feet should be ok for most activities.
If you're looking at knee-thigh deep and bathtub sized, as long as you're fairly fit you'll be able to dig it by hand. f you're going for waist-chest deep or more, consider hiring in some machines or booking a contractor to dig a "backyard pool"
What are your ground conditions like? A pit big enough to wallow in is digging a few tonnes of dirt minimum, add in tree roots, rocks, hard packed dirt or sticky clay and you're set for some hard (but rewarding) work.
How high is the water table? How much rainfall do you get? Is the soil free draining? Makes a big difference to how heavy the dirt is (or if your hole will fill with water while your digging it).
How strong is your soil? Could the sides of the pit collapse as your digging? (Not a problem if your waist deep. BIG BIG ***BIG*** problems if goes when your shoulder deep and squatting down to pull out a rock)
You'll want to think about a cover for your pit too- keeps the wildlife out, stops the top the pit drying out in the sun, and hopefully stops anyone falling in it.
Also have a quick brush up on your local planning rules/H.O.A rules- the last thing you want is falling foul of pen pushers or some nosy twat with a clipboard.