There is a lot written on the WWW about what oil to use in your classic vehicle. There are two important things you should do. First stick to the SAE weight specified in the service manual. The weight of oil you use in anything depends on the engineering requirements for the operating temperature of the oil. So the hotter you run the oil, the thicker it must be. This is why you see such high weight oils used in Racing where the oil can exceed 300 degrees. For the little 134's if the Ambient temperature is not going to be lower than 32 Deg F, the weight recommendation is 30W. If it is going to be colder than 32 but not under 10 the service manual recommends 20W. If it is going to be -10 the recommendation is 10W. Finally if it gets colder than that, 5W. Second it needs to have a high wear additive (ZDDP). So a good High ZDDP 10W-30 will work well for most of us. The 10W indicates additives that make it work in the cold environment needed for 10W, as well as the warmer weather 30W requirement. No need to worry about multi viscosity or straight weight, either will do as long as the SAE weight is there for the ambient temperature. The "cold weight" number (the 10W in 10W-30) is the additive package extending the range of the oil.
So for mine I use Valvoline VR1 10W 30. This is about the highest load capable, high ZDDP street-able oil I could find. It proves out on top in testing. One of those can't go wrong oils. There are a few brands however that will work just fine.
The most important aspect of the oil in a classic flat tappet engine is the amount of Zinc it contains (ZDDP). There are two things that need attention. The camshaft lifter design requires a high wear protector (Zinc). The low oil pressure inherent at idle, requires a high film strength. Finally if the engine sets a lot, a good anti-rust additive.
I would not use the synthetic version of VR1 or any synthetic. You would have to be very sure the piston rings and cylinder finish, seals, gaskets and sealants are compatible, before considering synthetics. Most oils intended for Diesel applications have ZDDP wear additives. They usually have way to much detergent for a gasoline engine however. This can cause foaming in the higher RPM environments of a gasoline engine, and starve the bearings. If you use a diesel oil, you must be sure it is compatible with Gasoline engines. There are some combination Gas/Diesel oils out there.
The high detergent oils are something to avoid for sure on anything that hasn't been completely overhauled. I have seen the results from lifting a couple quarts from the old man's case of Castrol, and putting it in a well worn 350. Leaks and blow by was just the beginning of the woes. When working at the Ford Tractor dealer, everything on the place received 15W40, from all the lawn tractors to the owner's wife's Saab. We saw premature bearing wear as a common problem with the early vertical shaft V-twin Kohlers , but it didn't outweigh the cost of keeping different grades of oil on the shelf.
You haven't said if you have a CJ or other Jeep - there seems to be a slightly different part number at KWAS for CJ vs. Truck/wagon filters.
I'd make a parts store run first - I can find filters for my 1951 F-134 at the local NAPA parts store. I'd look at an STP Oil Filter P7FF; about $10.00. Make sure you get a set of gaskets with the replacement canister.
If you have the Fram style filter canister (the one with the bracket welded to it not straps) it is a NAPA FIL1010 or a WIX 51010. In the photo on mine one bolt ear has been cut off by the prior owner. There should be 4 bolts holding it to the bracket on the motor.