The crank puller/extractor, the threads between the inner and outer parts, will probably be bone dry. Some good grease on those threads (wheel bearing grease is fine), or anti-seize if that's what you happen to have, will work wonders in reducing the force you need to turn to pull the crank loose from the spindle tapers.

Hard to go wrong with Park Tools. My crank puller is different, bought at bike shop in the '80s before I knew about Park, but it's still going strong, nice hard steel, not complicated, and includes a double-ended socket for the two common bolt/nut sizes, and crank handle, no other wrenches needed.

I actually already had a crank puller bought years earlier, but it was for a French bike, and that didn't fit the vast majority of crank threads. Still have that French size one in my toolbox.