One of the great things about hearing a truly great system is that (aside from live music) it gives you a reference point at which to aim. The fact that your friend is nearby and good enough to have you over means that as you sample different products and grow your own system you (and he) can check your progress against what he has going on at his place.
Money matters but not as much as some people think. Component synergy is very important. Finding products that complement each other is key. So is the room. I've heard very expensive systems sound very mundane in a bad room (or one which does not allow optimum placement of equipment and, particularly, speakers). I've heard modest systems that sound wonderful because they are positioned correctly in a good sounding room and the component parts have been carefully selected.
Venture forth, try new things. Keep refining your plans as you learn and try to anticipate where you are going. Avoid relying on other people's opinions, trust your ears. You know what sounds good--you heard it at your buddy's place. My stereo is still not where I want it to be and I've been evolving it upward for over 20 years. Folks on the Audiogon have been a huge help and I've invested the time to experiment and listen.
On the narrow point of what to change, I'd agree with the others who say start with the speakers--the transducers matter the most (despite what the folks at Linn used to say!). Set a budget, take your time and listen to everything you can. If you don't find anything at your price point that is significantly better than what you have wait until you have more money and then go listen again. It took me two years to find my current speakers and a year to find the one's before these. I think you can get very close to what your friend has if you are patient and willing to do the leg work.
Last thought: consider a pair of Harbeth Super HL5's. A peruse of the Harbeth users group will reveal that many folks are using Plinius amplification and are getting great results. The entire Harbeth line is phenomenal and the HL5's will, unless you have a very large room, have enough bass to give you the bottom end you are looking for. Get some nice (Sound Anchor) stands and set them up right (with lots of air around them). With the exception of frequency extremes and that last touch of detail and realism you may get pretty close to where you want to end up.
