Which is the most important part of a stereo system?

It’s called a credit card....get one with zero percent for 21 months....then you can get a 2500 to 6000 dollar amp...credit cards are good tools if used wisely and lots of them give generous points back on purchases well a as a nice sign up bonus. For instance spend 1000 get 250 back or spend 500 get 150 back.....Like getting a nice discount on what you want. At 21 months @ zero % I’d say that’s a pretty nice deal. If not paid in 21 months, just transfer remaining balance to another good card offer and so on and so on....I always read posts whereas the person says I’ll never be able to get this or that etc...well you can if you use credit responsibly. Another good example is Music Direct. Every holiday they run a 0 % financing for up to 3 years!... probably the best deal in town. But, I guess I can see how some are afraid of debt...you only go this way once, life is short etc etc 😁

Audioguy is correct. Get 4 to 5 high limit credit cards with cash back or some kind of rewards. Max them all out on some high end audio gear. The amp is 10 grand but you make 60 grand a year? No problem use the card. Speakers 10 grand? Not an issue. Max another card out. Its the most important part of my system. 

If you are going to buy on credit, at least make sure your home or renters’ insurance will cover said equipment in case of theft, power spike (or good surge protection) fire or other act of God. 
I’d hate for anyone to be paying off debt on something they don’t even own anymore or can’t use. 

....and jeffvegas lives in 'a van down by the river'...

A highly armored one... *tease*  It's best to stay mobile with max'd cards....;)

There is no most important component. They call it a stereo “system” for a reason. My own approach is to figure out what the weak link is and address that next. It’s a never-ending project and the improvements get smaller and smaller but my ability to hear them gets better and better. 
That said,I can remember getting three big jumps in SQ over the past 20 years, that you might cogitate over before chasing boxes. 

1. A hospital grade wall outlet. A genuine WTF moment. No PC ever made as much difference as the outlet itself did.
2. Antivibration under the pre-amp. Iin my system it has mattered there more than anywhere else.

3. Perfect Path contact enhancer applied as the maker recommends it. An astonishing product, but you’ll never find it again. The maker died this winter and apparently the formula passed on with him. The entire community should be sad about that one. It turned out I purchased one of his very last tubes. 
but that is with my system. For someone else it might be something else. Tthere is no magic amp or pre or speaker out there that will transform a system. 
I could add a fourth — a well produced  recording. The better your system is,the more you are at the mercy of the production quality of whatever you’re listening to.