Most people anymore will take the western port because it is typically a lot easier and faster to take than trying to knock out the other three ports or get them isolated.
if you rearrange your support units in a timely fashion, i.e. mostly pioniers and the heavy siege artillery, plus maybe put Model in command of one of 18th Army's corps, you stand a good chance to take Leningrad by brute force. The German formations are just that good. Even if there is level 3 or better forts built up to protect the route to the Western port and even the river's southern hex, it remains feasible. It can be very costly.
I usually also go for the Eastern ports, though, since I want to connect to the Finns coming down East of Ladoga and want a chance to hit Tshikvin and severe the railroads as far East as possible. That lends extra security to the Volkhov line during blizzard as supply will become more of a problem for the Reds. However, I also have found myself so late reaching Leningrad that taking the Eastern ports would have come close to mud and blizzard, and with the river in the way, I suddenly had some Panzer divs in poor supply across the river. Very useless waste of assets, though not dangerous.