Still haven't sorted out the idle problem?... :o(

Anyway, when changing rim size, you should always maintain the same
wheel size (rim + tyre). So when going up in rim diameter, you must go
down in tyre profile (tyre profile defines tyre heigth in percent of
tyre width, i.e. a 195/65 tyre has a width of 195 mm and a heigth of
126,75 mm).

You can then play with the combination of rim diameter, tyre width and
tyre profile. From the standard dimension of 195/65R 15 you can go to:
195/60R 16
205/50R 17
225/45R 17
195/45R 18
225/40R 18
195/40R 19
225/35R 19

So, the maximum size of rim is really a matter of taste (handling vs.
comfort, economy vs. look). The 205/50R 17 would be a good compromise,
and the 225/40R 18 would be more sporty but with less comfort.

Try to look at http://dunlop.tiremanager.de/eu_en/default.aspx?action=SelectSearch&case=model&m
odel=E-Klasse
, select your model and look at the "tuning sizes" to see various tyre
suggestions and at "tuning rims" to see various rim sizes illustrated
on your car.

You should know that rim size has three dimensions, diameter, width
and offset (fx. 17" x 7½" ET 49).

The offset (ET) is how much (in mm) the rim is "pressed in" with
respect to being centered on the mounting flange. ET 49 is standard
for W124. You can play with tyre width and ET to get the tyre flush
with the chassis, which gives a much sportier look (smaller ET brings
wheels outwards). And you can lower the suspension by some 35 mm by
replacing springs, which would look nice with your new rims - but
again comfort vs. handling/look.

And by the way, you should choose a rim with that suits the tyre
width. With the suggested tyres a 7½" rim would be fine. I you want to
go wilder (such as 255/40R 17) you should use 8½" rims.

In any case, when you play with tyre width, wheel offset and lowered
suspension, you shall observe the space in wheel wells and how the
wheels will pass the fenders when turning.