I've had subscriptions to three newspapers on the Kindle, and they are all a bit different. All share the common feature of the front section having headlines and the first three or four lines of the article. What I do is move back and forth between this section and the articles (using the Back button to return to where I left off in the front section). At the front of each article is a next article link, so it's also very easy to just jump from one article to the next after the first paragraph.
The New York Times has pictures, the L.A. Times doesn't, so that is a consideration. Also, they don't send the comics or the crossword puzzles, so you'll miss those.
Right now I have about three months of the L.A. Times on my Kindle (I deleted older papers manually, but theoretically they should be available forever once downloaded), and the search feature is pretty quick. I can search through every book and newspaper on my Kindle in about a minute.
Topher