The engine in your Jaguar - six or twelve cylinder - is recognized world-wide as a pargon of durabilty. With proper routine servicing these engines are known to last 150,000 or more miles without overhaul... or significantly less if neglected. Regular oil and filter changes are one of the best ways to ensure long engine life.
It is almost universally accepted that the engine oil and oil filter should be changed every 3,000 miles (4800 km). In the 80's Jaguar followed suit with many manufacturers and recommended a 7,500 mile interval under certain conditions but it is doubtful that you'll ever find a Jag owner waiting that long, and neither should you.
Castrol seems to be the motor-oil-of-choice of many Jaguar owners but, in fact, any name brand, premium grade oil is fine. Nobody puts cheap oil in a Jaguar. According to the Jaguar service manual, anything from 5/30 weight to 20/50 weight is acceptable depending, of course, on temperature and driving conditions. The majority of Jag owners, especially with higher-mileage motors, use 20W50 for all conditions except winter driving with temperatures near the freezing point when a switch to 10W40 is made. There is ample discussion of motor oils in the jag-lovers archives if you are interested.
Some owners prefer the use of synthetic oil. The relative pros and cons have been discussed at agonizing length over the years. Search the archives for details, but, in a nutshell, synthetic oil seems to work well except for a greater tendency for it to leak past gaskets and seals.
The oil filter should be replaced with each oil change. Although pre-1975 (?) Jags used a cannister type filter, most Series II cars and all Series III cars use a conventional spin-on filter. Many owners question where to buy filters and what brand to use. The factory type Jaguar oil filter (EBC9658 for all "spin-on" applications) would certainly be a good choice and can be purchased very reasonably from most Jag suppliers. You may want to keep several on hand.
The Bosch 72147 is also popular with many Jag owners. I have heard, but not confirmed, that the Bosch filter and the factory Jaguar filter are identical except for labeling. More commonplace alternatives would be the AC Delco PF964, the Fram PH2995, the Purolater L30381, or the Lee LF2818HP. Once again, the jag-lovers archives runneth-over with discussion of this topic.
Different sources cite slightly different sump capacities. The Series III XJ6 owners manual calls out 7.75 US quarts, the service manual says 17.5 US pints. My own experience is that 8 US quarts (7.5 L) is just fine. Similar discrepancies appear for the 12 cylinder models, with 11.5 US quarts (10.8 L) being typical. No matter - after changing the oil and running the engine for a while, you'll always double check the dipstick anyway, right?
While changing your oil take advantage of the opportunity to top-off all fluids and give the car a good visual inspection. See other "routine service" pages for specific items. Soon enough you'll establish a methodical "oil change drill".