the original Pirelli tires are very tall and they make the car sit high, I'm used to mine being lower by about 1" inch. (compare the height of both my cars side-by-side in the picture and you can see the height difference in the door mirrors, about 1"). Otherwise, with factory-size tires, both cars are identical in height.
Replacements depend on the wheels you finally decide to use, but wider and lower tires are nice, the car handles so much better and "flatter", also there's less body turbulence at interstate speeds above 70mph, because the car is lower, makes a giant difference.
I like Dunlop tires, they are not so hard like Michelin, not slippery in rain like Pirelli, not noisy like Goodyear, do not explode like Firestone/Bridgestone, and Jaguars came with Dunlops since the early 1950's, so after using Dunlop SP Sport M2, (no longer made), I plan to find Dunlop equivalents. You could use size 225/60/*R/15, not as fat as the 235 I use. Forget about wasting money on "run-flat" tires or "nitrogen-filled" tires, or giant white-lettering tires. It's all sales gimmicks and I for one, wouldn't trust my life to a nitrogen-filled tire, no thank you!!
Unlike most everybody here, I like the wide whitewall tires, like those in classic cars, I saw a Series 3 XJ-6 with wide whitewalls and it looked awesome, but your car would also look good with thin Redlines or just plain blackwalls. However, Redlines with Gunmetal Grey look awesome.
I'm sure others have their preferred tires, some I may have never tried in my cars.
you can check Coker tire in Chattanooga for thin radial Redlines and wide whitewalls, otherwise forget about TireRack, it's useless.
Ex