Which is the most important part of a stereo system?

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.

The room. 
I’ve head so-so systems sound wonderful in a great room and amazing gear in a poor room sound meh. 
Everything matters absolutely but the rooms acoustics make it all possible.