The inner part of the clutch (has three small metal buttons on it) should spin at the same speed as the outside of the pulley when the clutch locks together (reasonably fast, crank speed.) If it isn't, then it shouldn't move at all when the clutch is disengaged. Spinning slowly all the time isn't a fialure mode I've seen before, but it sounds like something is off.
First and foremost, are you competent to do your own diagnosing/work. I only ask because until I dug into my AC system, I knew plenty about cars and precious little about automotive HVAC systems. I kinda jumped in the deep end, and with the FSM and some members here I figured it out.
If you're going to do this yourself, first thing in my mind is to get a gauge set on there, and verify you have good pressures. If the compressor won't engage and cycle, verify that you have enough static pressure to engage the system (too low pressure, compressor won't engage the clutch). Also get someone to cycle the button on and off while you're in the engine bay and listen for the compressor relay to click on and off.
That should get you started. If any of this sounds intimidating, don't be ashamed to bring it to a pro. AC work can run into the high hundreds/over a grand very quickly. I did all my own work/bought gauges and vacuum pump/bought a few tools and I was into my job $700 (compressor, condensor, drier, expansion valve, gauge set, vacuum pump, line flush, recharged myself, everything.) Compare $700 to $1200 to have a shop do it. If saving $500 in labor is your intent, keep posting back and I'll try to help walk you through this. Also, search through Phil's AC Hell Thread here on the forum.