Changing shocks...
 

Is there anything I need to know/buy other than the shocks themselves?

Am I just taking the old ones off and putting the new ones on?

On My W123 on the Rear I had one of the Bolts that holds the Shock on break off.

I attempted to use an Easy Out type Tool on it but that did not work and I ended up drilling out the hole and tapping it for a larger diameter US thread size Bolt.

I also had to enlarge the Hole in the Shock that the Bolt goes through.

I assembled the Bolts with an Antisieze Compound so they woulr not rust again.

The fronts are actually struts so they are a bit different than the 123 cars.

For the fronts there are upper strut bushings, bump stops and dust covers that might need replacement.

Sixto
MB-less

I snaped a Bolt of on the rear on a W123
http://www.peachparts.com/shopforum/diesel-discussion/353497-w123-sheared-off-lower-sock-bolt-head-drill-out.html

Also I needed to remove both Seats to get at the top of the Rear Shock.

I also broke one of the bolts, luckily there was enough bolt left to weld a nut to it

I don't know about your car but some use the shock as a suspension droop limiter. ( front W202 C class 95 - 00 ) so the lower control arm needs supported to take the pressure off.

If you are doing the fronts you will want to replace the bump stops and strut mounts. On both front and back you will need to support the control arms with a good jack. Failure to do so may jeopardize your life.