How much pump flow does a homemade backhoe actually need?

Short answer: pump size is mostly about speed, not force. Cylinder bore sets the force and the pressure you'll need, but flow sets how fast everything moves. The math is easy once you pick your cylinders: bore area times the speed you want equals flow needed. Do it for the boom cylinder since it's usally the biggest, and remember to check the rod side separately if you're extending and retracting at diffrent speeds. Most compact tractor PTO pumps run somewhere around 5 to 8 gpm depending on the pump, so if you want the boom to cycle in a few seconds, do that calculation before buying anything. Also make sure the pump is rated for continuous duty, not just intermittent, because digging means holding the relief valve open a fair bit. One more thing on the hydraulics that nobody tells you til it's too late: put relief valves on the work ports for the boom and dipper. If the bucket ever gets pinned under something and you move the lever the wrong way, dead-heading the pump or overpressurizing a hose gets expensive fast. A control valve with adjustable reliefs on the A and B ports is cheap insurance. On the stabilizers, manual legs are fine for what you're doing. I dug stumps and a few hundred feet of trench with flip-down legs clamped to the three point arms and never regretted it. The machine just isn't heavy enought or the forces high enough to matter for occasional use. What does matter is getting them out wide and solid so the back end doesn't walk sideways when the bucket bites. If you find the legs lifting or the tractor shifting on you, that's the day to think about hydraulics, not before.

Biggest warning I'll give: your backhoe mount and the front of the tractor take more abuse than you expect. Hook the bucket full, curl up on a stump, and you'll lift the front end clean off the ground if you're not braced. Some folks put weight or a loaded loader bucket up front to counter it.

Following this one since I'm doing somethig similar with a small trenching rig I built last summer. I skimped on the valve side of things and bought one of those cheap lever valves off a supplier site, and the arm moves fine but it creeps down when I hold it up. Been told the valve is leaking internally. So my question is, does the valve quality matter as much as the pump and cylinders, or is some drifting normal?

I'll push back a little on the 'manual legs are fine' take. Sure, for a water line trench you'll get away with it, but the first big stump I pulled on my little Kubota bent the clamp on my flip-down pad because the whole back end pivoted on one leg when the bucket bit. It's not about forces being high, it's that a manual leg can't take the side load when the tractor rocks. If your mounts are welded pads instead of clamped, different story. Clamped on, I'd go hydraulic or at least weld up a proper bracket.

Been down this road back in the 80s with a gas engine pump rig, before I ever heard of running one off a PTO. One thing I learned the hard way: keep your hoses big enough on the suction side, not just the pressure side. I starved a pump once with too small an inlet and it howled like a banshee and ate itself in a season. Also on the PTO side, check what rpm your tractor makes rated flow at. Mine only hit full output near 2000 rpm, and digging at low throttle gives you half the speed you figured on.