I think the best word to describe The West Wing would be 'charming'. The creator of the show and writer of something like 96 of the first 98 episodes is Aaron Sorkin, the guy who wrote The Social Network so the dialogue is about as witty as you'll get on television or anywhere else for that matter.
The episodes in the first two seasons are fairly self contained (still have a number of mini arcs though) before they move into the re-election of the president thing. They also start some major arcs late season 2 that last for a most of the series so it builds up some fairly big storylines. Later on (season 4-5 onwards) it becomes a lot more one big story especially after Sorkin leaves the show when leading to a shift towards more character based stories, the trasition works well and isn't too dramatic a shift that it changes what made the show great.
The acting is great (most cast members won an Emmy for their acting at some point in the series) and the characters likeable. One of the benefits of being a long running series I think is that it means characters can evolve and develope at a good pace: nothing feels forced or too sudden. That being said, the show was notorious for having characters simply disappear though for the most part it doesn't happen to anyone of any major significance.
If you like politics then this is pretty obviously a good show for you to watch. The show ran from 1999 to 2006 if memory serves so obviously there were some pretty major events in there (in the real world) that are reflected in the show with story lines often in a similar vein to real world issues past and present. At times the writers are clearly voicing their opinions through characters (at one episode that was written not long after 9/11 one character makes a rather obvious speech about religious fundamentalism but for the most part I agreed with the opinions of those writing it anyway since it approaches the world from a fairly liberal perspective. A number of characters are based off real people (the deputy chief of staff is based off Rahm Emmanuel, the Republican candidate against the president in s3-4 is based off Bush, Jimmy Smits' character is based on Obama) while the president is really more of a representation of what Sorkin thinks a president should be like.
Overall it's a great show, the main highlights for me are the amazing dialogue, likeable characters and the impressive production value (it looks much nicer when they change filming style in season 3). At times the show can deliver some pretty devastating blows drammatically which I think is a testament to the quality of the writing. Yes it is a long series but it does follow the natural progression of the presidency since the series starts one year into the administration and ends 7 seasons later at the end of the presidency (the last season and a half focus mostly on the next presidential race). Definately worth checking out.