That looks like a fairly decent car to work with!
It's already been driven 7 miles home, so there's no need to concern about damage, what's done is already done.
Biggest place to look for wear is where the rocker arm rubs/rolls on the valve tip.
Rockers on a bigblock are 'sloppy', where they fit on teh shaft, and also side-side.
As mentioned, a valve got stuck. I suspect the cam can push the valve open with more force than the spring can close it, so the valve sticks open. What then probably happened was the pushrod retracted and the valve didn't, and the pushrod fell from the rocker, and got pushed against somethign immobile on the next pass.
I've had quite a few engines like this that still had life left in them. I've seen them with sludge 10x worse, too.
Check timing chain slack: remove the dizzy cap, put a socket on the crankshaft bolt and rock the engine to/fro 30deg or so to see how quickly the distributor rotor responds. This is the easiest time to check this, as you'll be taking the distributor and oilpump driveshaft out next.
Put some clean oil in it, if you're on a budget use oil-change oil from your daily driver if it's a well-maintained engine.
Do an oil pressure test - install a gauge at teh port at the rear of the engine (there are 2 of them), remove the distributor and oilpump drive shaft, and spin the oil pump the correct direction with an electric drill. (removing the shaft generally takes LONG needlenose pliers and can be a PITA in a neglected engine) Pay attention/make notes on where the slot was pointing, and at what angle the slot was pointing when it came free (it rotates as it is removed due to the gear teeth)
Run the drill enough to watch for oil flow out of the rocker shafts and onto the arms.
If oil pressure and the flow to the rockers is OK, and if the engine didn't smoke on the way home, presume it healthy enough to invest in it further.
Replace the pushrod and timing chain and plan on some frequent oilchanges (every 2-300 miles?) to help clean it up. You could swap a pint or quart of ATF into teh new oil to help clean, ATF has more detergent than oil. You could also use Marvel Mystery oil. I would avoid any 'motor flush' treatments as cleaning sludge out too quickly can cause it to go someplace harmful and block oil flow.
When you have the rockershafts off, be aware they must reinstall properly, there's an oil hole that must be in the correct location or it will reduce flow to teh rocker arms/valves. (you can google that)
Another thing you can do - if the rocker arms/shafts are removed, insert an airline fitting into the sparkplug hole and pressurize the cylinder. You can rap each valve tip with a small deadblow hammer and see if you get a resounding pop of air out of the port, and if the valve closes. This will help find if any other valves are sticky, and the cylinder's air will help blow out any debris that was laying around the valve seat (although that likely blew out on your drive home). You may find most of the valvestem seals are broken or missing, so you can squirt some oil toward teh valve stems before rapping the valves if you wish. Would be a good time to change seals, they are cheap. You can also listen for escaping air to determine if you have any valve sealing issues - if you have a burned valve it will be a constant rush out the intake port or the tailpipe. In an engine like this one, you should expect to hear blowby leaking past the rings into the crankcase. Don't get hung up on that - the main thing to check is for large leakage out the valves.
An alternative cleanign method:
Get the shopvac out and a small screwdriver/small brush and clean as much sludge out as you can (within 1-2 hour timeframe is sufficient) - make sure any chunks you break loose get vacuumed out immediately - don't lose them inside the engine. Do the heads and lifter valley.
A squirt-bottle of kerosene, diesel, mineral spirits, etc can be used to rinse stuff away. Old toothbrushes are economical.
Drain the oil pan, put the plug in and rinse some solvent down the lifter valley. You can let it soak and then drain it, or let it run out as you go.
When you change the timing chain, the front edge of the oil pan will be available for pan-rinsing also.
Don't use your your favorite/clean shopvac for this unless you plan to clean it afterward. (I have a 'junk' shopvac specifically for such work)
Whichever you do - plan on doing some frequent oilchanges for awhile. You can always pull a valve cover to look for cleaning progress as you go.
Rock Auto will be a good place to look for individual pushrods, valve seals, and possibly the rocker arms if you need any.
Keep us posted on your progress!