For the Oil filter adapter I would use the Fiber gasket as the Rubber one is for the Air cleaner to carb.
Best Gasket website has the list of parts:




QTY       PART NO    CONTENTS
1             133               Oil Pan Drain Plug
1             175               Oil Pump Inlet Tube to Pan Seal
1             235               Oil Pump Relief Valve
1             275               Oil Pump Inlet Tube Seal
1             6286             Valve Stem Seal
1             1186             Oil Pan Drain Plug
1             1289             Down Draft Tube, T-Bird
1             1347             Oil Filter Mounting Bolt
6             1382             Push Rod/Valve Cover Grommet
1             1474             Oil Pump Inlet Tube Fitting
1             2002             Fuel Pump Bowl
1             2087             Fuel Pump Bowl, 54
X  1         2142             Fuel Pump Bowl, 55-57 T-Bird
1             2306             Fuel Pump Mounting
1             2313             Oil Pan to Inlet Tube
1             2331WP       Water Pump Bypass
1             2331             Oil Pump Screen Cover
1             2364             Crankcase Ventilator
1             2379             Oil Pump Inlet Tube Flange
1             2391             Timing Cover Seal
1             2458             Oil Pump Cover-Rotor Type
1             2837             Rear Main Cap Seal Kit
3             3228             Exhaust Pipe Flange
3             3346             Exhaust Pipe Flange
1             3424             Oil Pump Cover-Gear Type
X  1         3452             Air Cleaner to Carburetor
1             3483             Crankcase Ventilator
X  1         4256             Carburetor Base
X  1         4257             Air Cleaner to Carburetor
1             4278             Water Outlet
1             4279             Oil Pump Mounting-Gear Type
1             4311             Oil Filter Mounting
X  1         4361             Oil Pump Mounting-Rotor Type
2             5106             Rear Main Seal-Rope
X  1         5152             Air Cleaner to Carburetor
X  2         6151A          Carburetor Base
2             7093             Water Pump Mounting, 55-63
1             12054           Timing Cover
1             14041           Intake Manifold Right
1             14042           Intake Manifold Left
1             17022           Valley Cover
2             18005           Valve Cover
2             18093           Exhaust Manifold
1             24026           Oil Pan
1             Pinsee Armin
1             99999***     Special Knife Set - see Armin

ENGINE REBUILDING SET
RS572G-2
Ford V8 312 1956-57
x - indicates where part is not always found in other brands' sets

This is the front of the oil filter spin-on adapter, the gasket in your photo (Best Gasket no.1347) is not used with this adapter, the gasket (4311) goes at the back between the adapter and the engine block.
see item 6838 and 6749 here:


As you can see the bolt (tube) holds the adapter plate and gasket to the engine block. The bolt has no gasket needed. 6749 is included for the older canister cartridge filter housing.
From Ted's Website:

WD40 is not a good oil. It’s a water displacement fluid. You can still wipe everything with it but I would wipe your cylinder walls with auto trans fluid Or Marvel mystery oil on a white paper towel Over and over until the paper towel stays red. Cam should have the recommended cam assembly lube and the rods/mains assembly lube. I use Lucas since I can find it. I use it on all metal to metal surfaces, push rod ends, Rocker tips, cam gears/chains. Etc... everyone seems to have their own opinions on this. Good luck

Different manufacturers do things differently for similar parts.  Your new oil pump has the hole for one of the spur gear shafts drilled completely through the block side of the housing while the older pump you have does not have that same hole drilled all the way through.
 
While we are on the subject of oil pumps, it’s prudent to disassemble any new oil pump and examine its inner workings thoroughly for any problems.  Be sure the oil pressure relief valve works freely.  If there are any machining chips to be found, the oil pressure relief valve cavity is a place where they can be hiding.  A good cleaning and some fresh lube on the gears and the pump is ready to be reassembled.