Well, if you want to catch up on Hawkeye’s life and feel really emotional and sentimental, I’d start with Hawkeye: Blindspot. (I haven’t read this because I can’t find it but SO MANY people say it’s the best). Someone told me once to start from Blindspot and branch out.
But well, if you want to go into the order of all of it and do what I’m doing, then begin with Hawkeye and Mockingbird (there are 6 of those) then continue on to the Widowmaker storyline (four issues).
In order to know about his past and his life, though, you can go for the whole Hawkeye Volume 3. The storylines High Hard Shaft (6 issues) and A Little Murder (two issues) are more along the lines of his background.
He was recently in his own mini series, Avengers Solo (I think there were four…) but I never bothered reading it because it got really, really bad reviews. Many said it was a waste of their time. But I guess if you want the complete package, you can chuck that in there.
Also, there’s another storyline in The New Avengers called The New Avengers: The Reunion and some people say it should be read before Blindspot. But if you aren’t familiar with his past, it’s best not to start there. It’s really cute. It’s the reunion of him and his ex-wife, Mockingbird.
Hmm.. I think that’s it. If I were you, I’d just have fun and experiment a little. And I hope this will help spread the Hawkeye love! Because personally, I think he’s very underrated and doesn’t get the appreciation he should.