I'd start with the n/s/r wheel (assuming it's a RHD car) and try and gravity bleed it. Clean & remove the brake fluid reservoir cap, check the fluid level & top up if necessary. Then clean & open the bleed nipple slightly with a length of hose attached and see if brake fluid starts running out. If it does, get your assistant to top up the reservoir continuously until you see nice, new brake fluid running out. Then do o/s/r, n/s/f and o/s/f
Check the front calipers to see if they have multiple bleed nipples. If they do, do the uppermost ones first
The reason to gravity bleed, and not pump the pedal, is that on some cars you introduce air into the servo & ABS and it tends not to come out again. If it won't gravity bleed I'd get an expert to do it with a pressure bleeder
Once you're done, and the pedal has hopefully returned, adjust the handbrake. I assume the W123 has rear discs. If it does the handbrake adjustment won't affect the pedal. If it has drums it will
If your reason to change the brake fluid is a soft pedal then you may have a leak, bad servo or bad master cylinder (or any combination thereof) and I wouldn't assume bleeding will cure the problem. In fact I wouldn't assume anything at all with brakes, particularly on a heavy car like a W123. Finally I'd have all four wheels off before you start and have a good look for fluid leaks. Once you start bleeding you won't know if the fluid round the nipple is from a leak or from bleeding, so check them all first
That's how I'd approach it, but then I normally get experts to do it for me. Hopefully some of them will chime in and correct any mistakes in my plan!
Nick Froome
www.w124.co.uk