I'm planning a similar upgrade to my 94 e320. If you are planning on doing the work yourself, I would recommend changing the speakers before the head unit because you can take your time and evaluate the setup and listen carefully. If you're going to pay someone to install the components, do it all at one time. This way you have minimum downtime and installation expense because they only have to take your car apart once.

I am not aware of the rated output of the stock Becker, but it would probably be sufficient to power an efficient set of speakers. Check the efficiency rating of the speakers you purchase. The best way to increase the sound quality of your system is the speakers. The Becker head units are on par with many of today's cheaper units ($200 and under).

Here is my story:
In my 86 190e I decided I needed more bass. So I installed a subwoofer in the trunk. It added bass but the rest of the system still sounded horrible. So I decided it was time to upgrade the speakers. I decided on a set of Canton RS 3.13's after auditioning many sets of speakers (I plan on installing these into my e320 now). The set consisted of three drivers per stereo side. A midbass driver (installed in the door), and a midrange / tweeter coaxial pair installed in the stock dashboard location. I used a pair of MB quart mounting adaptors for the door which seemlessly allowed me to mount the woofer in the doors' armrests. The set was powered by an Alpine amp in the trunk and sent to the speakers via trunk mounted crossovers.

Ok, the moral of this story was that I didn't have the money to upgrade the head unit so I simply ran all of the necessary wires to install a new head unit when the money would be available. I used the stock Becker to power the rear deck speakers and provide the source for an amp for the front speaker set. The system was a huge improvement on the stock system.

Then about a year later, I added an Eclipse head unit based on reviews and listening tests in stores. When I got it installed, I found that the Becker actually sounded better. Two months later a swaped back the Becker and sold the Eclipse.

So, to make this long story longer, do all of the work at once that you can afford (time and money). If limited by anything, change the speakers first. Use your ears as judge, not other people's opinions.

Good luck. I'd like to know how things turn out.