I had the pleasure of owning a '76 PA28-140E for 4 years (I now own and fly two Beeches; a C23 Sundowner and a 77 Skipper; the Sundowner is for sale).
First of all to correct some misinformation: not all Cherokees had the roof-mounted trim. My late-model Cruiser had the trim wheel between the seats, just like a Cessna.
The flap system is a joy to use. My Skipper has electric flaps and I hate them. Takes forever to go down or up and you'd better practice flapless landings, you never know...plus the indicator is lazy making it impossible to accurately gauge when you have the right amount of flap applied; therefore I use either no flap or full flap on the Skipper (only 2 knots difference in stall speed between each configuration). Manual flaps on the Cherokee: you can feel which notch you're in, and flaps are available (or removable) instantly, it's simple, relatively maintenance-free. Crude, but damned effective.
Speeds: book approach speeds are 85 mph no flaps, 82 mph first notch, 79 mph second notch, 76 mph full flap. Carry too much speed and it will float. Too little and that little 150 hp Lycoming will have trouble keeping you out of the backside of the power curve. Not a great glide ratio either. Like others have said, haul WAAYYY back on the stick on landing. Keep in mind that this bird, with only the front seats occupied, tends towards the very front of the CofG envelope. Put two people and full fuel on board, and you will actually be forward of the CofG envelope. It's flyable in that configuration but caveat emptor: it's illegal and voids your insurance. Best to have that proverbial case of oil in the luggage compartment (which is not overly large...if there is one, many Cherokees do not have ANY luggage bin).
One thing to keep in mind, the tail is a stabilator, not a conventional stabilizer and elevator. Doesn't make much difference but on a slow landing, forward CofG, I have managed to stall the tail before the wings resulting in a very inelegant, and potentially dangerous, three-point landing.
I find book speeds worked best for approach and landing. However if you have one with the STC for Hoerner-style wingtips (mind did), you can shave a mph or two off the book speeds for some really impressive short-field landings. But beware the tail issue mentioned above.
At MGTOW it's not a hot-rod on takeoff and climbout. Mine fairly had to be coaxed in the air, as it had a cruise prop. Once in the air, decent cruise speeds are possible in spite of the aircraft's reputation. I could make 128 mph on 8.5 gal/hr. Pushed, it'll even break 130 mph. My Sundowner with 30 extra HP does no better, maybe even slightly worse.
For those who say it's "spinnable", beware: if yours is a model with a built-in ventilation blower in the tail (or worse, air con), it is definitely NOT spinnable, the CofG is too tail-heavy and it risks flat-spinning. I have heard a horror story of a flat spin with the rear seats occupied, had to push the door out against the slipstream to add enough yaw to break the spin. Urban legend or not I do not know, but it's enough to make one take notice. Hard to spin to the left. Easier to the right, if memory serves. Tends to spiral dive rather than spin. In any case, I can't say this too loudly: CHECK PLACARD BEFORE YOU SPIN, to ensure yours is indeed "spinnable".
I kind of miss mine, fairly cheap to own and operate, very reliable if not very entertaining bird to fly. The Sundowner is much nicer to fly but the 10.5 gallons per hour is getting very tedious with 100LL at $1.40/liter, hence the recently acquired Skipper (slow though! 90 knots on a good day).
Mike