I'm writing my query letters, and I'm not sure if it is appropriate to mention why I am sending a query to these particular agents. Of course, I know that they represent authors whose books I've read, and have sold books in the genre that I'm writing. Just as importantly, I liked what they had to say on their websites, or in articles that they have written. Do agents care why you are sending them a query - whether you simply found a list of agents or have reasons that you would want them in particular to represent you? Is there a way you should mention that you believe they are people you could easily work with, or should you just not mention it at all?
Also, if an agent requests a query letter, synopsis, and the first three chapters - do they read the synopsis or the chapters first?
If you liked what someone said in an article definitely mention that. Less so the website cause chances are the agent didn't write all the stuff that's on it (particularly at a multi-agent house). And clients and books are fine to mention if you've read the books. I can't tell you the number of time someone has said "I see you represent Forrest Gump, so I know you'll like my book about tree surgeons". Sometimes I think it's the latest test from the New York Department of Mental Hygiene and I've failed ...yet again.
And I've also gotten those generic letters that say "I've sent this to a few select agents"...don't do that. And "I'm sending this to you cause you're a well known science fiction agent"...think again bucko.
The writing may be grand but they've raised the hurdle on whether I want to work with them cause it looks like they are absolute nitwits.
And don't mention you think they'd be agents you could easily work with; we assume you think so when you query.
In general you don't have to come up with a reason you're querying. We know why; you want us to love your book. That's all it takes really. The personal connection thing is nice (oh! she read my article in Poodle Pyrotechnics about the Dog Days of Fiction!) and it shows you're doing the reasearch but if all you said was "here, have at it, it's a mystery, 83,000 words, first person POV" I'd still read your pages.
And for the second question: skim the cover letter, read the pages, look over the synopsis in that order. Remember though, I don't ask for a synopsis and three chapters in the query package. Other agents do. A very astute comment to an earlier post pointed out the importance of all three of those documents working together.