Undercover is terrible. Worst of the arcade-style NFS games.
If you would go with an arcade NFS I would go with Most Wanted or Underground 2, but those probably are not compatible with the newer consoles.
Shift is a simulation style NFS. If you think driving is keeping your foot on the accelerator the entire race, you will not like Shift. However, for those people who understand how driving works, Shift is a very excellent game, but I would take Race Driver: GRID over Shift any day.
Hot Pursuit is not like the older NFS Hot Pursuits. The cars all feel the same, everything is quite arcadey, and I would be willing to overlook all of that if it wasn't for the extremely annoying, long, unskippable intro cinematics to EVERY FREAKIN' MENU AND RACE!
I JUST WANT TO RACE DARNIT NOT SIT THERE FOR THREE HOURS WATCHING MY CAR JUMP OVER A BRIDGE NINE FREAKIN' TIMES AHHHHHHHHHHHHHHHHHHHHHHHHHHHH HHHH
OH HEY I JUST GOT THIS NEW CAR OH WAIT I HAVE TO WATCH A 3 HOUR ADVERTISEMENT ON HOW AWESOME THE CAR IS AHHHHHHHHHHHHHHHHHHHHHHHHHHHH HHHHHHHH
I JUST UNLOCKED A NEW RACE OH WAIT I HAVE TO WATCH A 3 HOUR TUTORIAL ON SOMETHING I ALREADY KNOW HOW TO DO AHHHHHHHHHHHHHHHHHHHHHHHHHHHH HHH
Go with Shift unless you don't like simulation. Then, go with Hot Pursuit.