Considering how long it's been since a 360 was in a Chrysler vehicle, I'm suspecting it's got some miles on it and that it's reasonably stock? IF you're in FL, normal 10W-30, 10W-40, or 30 would probably be good. If "chasing zddp", then a diesel-spec oil can do that, which would mean Delo 400 or Rotella T in 15W-40 (dino) or 5W-40 in their synthetic variations. EITHER of these should be available most anywhere, by observation.
Check
www.bobistheoilguy.com for "Virgin Oil Analysis" to see postings of oil analysis, as to additive levels (zddp, calcium, etc.).
When I bought my new Brand X car in '77, after about 3000 miles, it was 1 qt down for the second time, so I was suspecting "an oil consumer". I put Castrol GTX 20W-50 in it and the consumption went to 1/2 qt down at 4000 miles. Everything felt fine, performance wise. When it was removed at 625K miles, replaced with a larger small block engine, I told the mechanic that oil choice for break-in was his. He, being an old drag racer, chose 30 Valvoline. After about 6K miles, I went back to the GTX 20W-50 and the throttle response felt a bit dull, in comparison. I ran that for a few thousand miles and then changed to 10W-40. The throttle response got sharper and more responsive, so the thicker oil was taking more power to pump. Then went to RotellaT 5W-40 and everything stayed the same.
Even the diesel oil has lower zddp than in prior versions, BUT it's still about 1200ppm (down from up to 1600ppm), so that's still plenty. LOTS of moving parts in those diesel engine valve trains! From the oil analysis reports, the "SL" ratings had 1000ppm of zddp, with the later "SM" and "SN" going down to about 800ppm range. So the current diesel-spec oils in the particular viscosities still have plenty of zddp in them.
As the oil blend stocks have improved since the first "wide viscosity" 10W-50 oils of 1969, the need for the thicker viscosities for "protection" has decreased markedly. Especially in the synthetics. Which is where the diesel-spec viscosities (15W-40 and 5W-40 syn) seem to fit nicely.
When I started using Castrol GTX 20W-50 in my '70 DH43N, that oil was mainly used in motorcycles, so finding it was a task. I'd buy it by the case until it came to be carried by more places, circa 1975+, so I know how much of a chore that might be. Whatever you decide on, having ready access to it can be important, PLUS a good price.
As for filters, rather than get a filter from the local Chrysler dealer, we'd get a Motorcraft FL-1A, which was readily available, pretty much everywhere. WIX is fine, too. Might shop for them online or via RockAuto, too, as you'll probably have more lead time in getting a filter than if you might need a quart of oil.
From my experiences and observations,
CBODY67