Here's what I'd do if it were mine....
a) Warm engine cranking compression test, Fully charged battery, throttle blocked wide open. Acceptable range 130-170 psi, no more than 20 psi difference between highest and lowest cylinders.
a1) If acceptable readings can not be obtained, rebuild is indicated.
b) If compression test is acceptable, drain oil and remove oil pan. Inspect main and rod bearings for wear. If the wear is not relatively uniform over 2/3 or more of the surface (less wear near the parting lines) then check clearance with a PlastiGage.
b1) If wear is abnormal or clearance exceeds .0025" for mains or .0026" for connecting rods then a rebuild is indicated.
c) If bearings and bearing clearances are acceptable, remove valve covers and check lifter movement at the rocker arm with a dial indicator and compare to specification for the camshaft being used. For a stock 289 2v/4v camshaft you should have no less than .2253" lift on the intake valves and .2325" on the exhaust.
c1) If specification can not be obtained a rebuild is indicated. Also, check rockers, fulcrum balls and pushrods for damage and wear and if adequate lift is obtained, correct as needed.
d) Remove water pump, fuel pump and front cover and inspect timing chain and sprockets for wear.
d1) If timing chain slack is outside specification (0.5" total at mid-point on slack side of chain) replacement of the chain and sprockets is indicated.
e) If everything, so far, is acceptable, you should have found the source of your noise. If not, and you suspect it may be a noisy lifter, remove the intake manifold and lifters and check them for bleed-down. The acceptable bleed-down rate is no less than 5 and no more than 50 seconds to bleed down 1/16" under a 50 lb weight with a 5/16" ball placed in the lifter cup. There is a special tool to check these (yes, I have one....) that looks like
THIS.
e1) If any lifters don't meet specification, disassemble, clean and re-test. If still unacceptable, replace. You must break-in the new lifter as if breaking in a new cam and lifters. If you see wear on the lifter feet and/or more than one lifter needs to be replaced you should consider replacing the camshaft and all lifters.
Okay, so assuming a rebuild is indicated I would remove the engine assembly and disassemble down to the "short block" (block with crank, rods and pistons still installed). I would bring this to a good machinist who will remove the cylinder ridge, remove the pistons with rods and crankshaft, measure the cylinder bores for size, eccentricity and taper and recommend an overbore size, and inspect and measure the crankshaft journals to determine if a polishing or grinding and polishing to underside is needed. You can also supply them with the cylinder heads if you wish to have them inspected for valve and valve seat wear, stem to guide clearance, pressure testing (Magnaflux if iron) for cracks, etc., and estimate repair.
Depending on the machinist estimates you can make a decision as to whether it makes sense to rebuild the existing engine or to replace it. One of the more common alternatives to a "crate engine" is replacement with a late-model 5.0 from a '97-1/2 & up Explorer/Mountaineer. Many of these engines have little wear and may need little or nothing in the way of major operations.... some might benefit from a new set of bearings but most won't need a thing. A new oil pump pick-up tube for front sump and the installation of your original 289's oil pan, front cover, valve covers, intake manifold and carburetor, exhaust manifold and a few other "conversion components" can have you back cruising for few bucks. This thread might be "enlightening". lol.
Got my GT40P up and running in my 66