Which component(s) benifit the most from isolation?

Different elements of a system benefit from different types of isolation, and the results are not always predictable. Also some manufacturers have spent time and resources experimenting and fine tuning isolation products specific to their components (eg AGD) whilst my impression is that some others just put some out there with little research simply to be in the market, and I'm convinced that some are merely snake oil. Also dealers want to make a profit on "upgrades" when folk can't afford to make a major component upgrade. Bearing all this in mind the ideal is to have home demos and try different things one at a time under key bits of gear, if you can find a dealer/another customer who will facilitate this.  Turntables often benefit most from isolation from/dissipation of low frequency resonances/disturbances (but there may be further benefits at other frequency ranges too), other items such as tube pre-amps and components with transformers may benefit from isolation/reduction of vibrations at higher frequencies or broader frequency ranges. I have a range of different elements across my system, and the effects vary from subtle to considerable to negligible, depending on the method and the component.

Components that MOVE the most benefit the most:  Turntable & Cart, CD Drive, Speakers.   

With that being said, current can make tubes and transformers, perhaps even cables, move a little.  So some folks report improvements when these items are isolated.  

As some have noted, above, improvements often vary with frequency as well as isolation method, mass of gear, etc.  

Your next-door neighbor's speakers.

Of course anything that has moving parts: speakers, turntables, CD transports, R2R decks, tubes which unfortunately are subject to undesirable movements ( microphonics). 
 

Many don’t agree w/ me but I’ve found over the years w/ several different systems that if the listening room has a very solid concrete slab floor or similar, it’s best to couple your equipment to it & let the mass of the floor / earth do the job. If it’s anything other than that , decoupling can be very effective & every component will benefit from doing so. 

All of it to various degrees. YMMV.