I've just finished the first series and I found it annoyingly cheesy.
Good on you. You'll rattle through the first four seasons like lightning, I'm sure. Persevere through the immediate post-Sorkin period, during season five, as it's the weakest the show gets, and it picks up a lot when it takes a completely new direction in seasons 6 and 7.
For pure enjoyment I don't think a show will ever overtake The West Wing for me. It just gives a warm, fuzzy feeling whenever I watch it through again (8 times and counting), and really does feel like I'm greeting old friends.
What are your politics? I find some people on the right make this accusation.
I do prefer the WW's altruism to the cynical, sneering stuff we tend to produce (cf, The Thick Of It). Just enjoy watching it more having someone to root for. Can't be sure what right wingers get out of it though.