There is one area that you probably will not match that old Pioneer, and that is tuner performance. For reasons that are beyond me, virtually all (I can think of no exceptions at the moment) manufacturers these days put poor performing tuners in their receivers. It would not cost much; a $100 Pioneer car stereo has a decent tuner, but a multi-thousand dollar home receiver has garbage for a tuner. So, if you use the tuner in that old Pioneer, you may want to buy a vintage receiver and use that until you want to have surround, and then use the vintage receiver as a tuner. Alternatively, you could buy a vintage tuner and a surround receiver now.
Also, if I am not mistaken, the Pioneer SX-780 was rated at a little more than 35 watts, though my memory could be off.
Surround receivers... Unless you are using low impedance speakers, I doubt there will be much difference between most $500 receivers in stereo performance. I do, however, strongly recommend that you only consider models that have a feature for automatically balancing the speakers, as proper speaker balance is essential for good performance. Without such a feature, you need a SPL meter and a tripod, and to take the trouble of setting this manually. You will have enough new things to worry about without needing to worry about that.
I also recommend that you get a receiver that has both the original Dolby Pro Logic (DPL), as well as Dolby Pro Logic (DPL) II and IIx. The reason to have the original is because films were mixed with a Dolby Pro Logic encoder, and were originally intended to be decoded that way. You might like the added processing of DPL II or IIx, and you might not. If you have it all, you can use whatever you prefer. Some receivers do not have the original DPL, just DPL II/IIx
When it comes time to set up your surround system, you will want to take a look at:
http://www.dolby.com/consumer/home_entertainment/roomlayout.html