but a new small stereo and connect it to my great old speackers

More information is needed.

Do you have a sub-woofer?

Specifically what output options (ports) are available on the new stereo and what inputs are available on/for the old speakers?

There are many online diagrams showing various audio connection options.

Take a look, sketch out your own diagram. Then look for the necessary cables and perhaps some adapters.

Still likely to sound different - "great sounding" will change.
 
Speakers haven't changed much since they were invented, as long as the speakers are within reasonable spec of the driving amp, ANYTHING will drive them.

Basic thing to know up front: 4 ohm amps can drive 4 or 8 ohm speakers, but 8 ohm amplifier cannot drive 4 ohms speakers, only 8 ohms.