Aha, I ran across this rundown recently. It might help.

Honestly, IMO the Marvel movieverse is different enough that knowing the comics is not necessarily an advantage. Widow was in Iron Man II, and Hawkeye is briefly in Thor (you do get a nice window into his personality there, if you haven't seen it yet).

There is a new Hawkeye comic going on now by Matt Fraction that's a fairly new take on the character (and more in keeping with the movies, as far as I can tell) that has been well-loved. The first trade is due out in March. The Brubaker Captain America issues coffeeandink talk about are also very good (at least the ones I've read).

Oh, and EDIT: Marjorie Liu's Black Window is indeed supposed to be good, I've liked the excerpts I've seen and I love Liu.

Edited at 2013-01-08 03:45 am (UTC)

I would probably say unless u really want to delve into the Marvel universe its going to be hard to pin point one thing to read to learn more about their relationship but i heard they're coming out with a movie more based around the two of them.

I don't know about comics canon, but the cartoon Avengers: Earth's Mightiest Heroes (Season 1 - 2010) is available on Netflix streaming here in Canada, is surprisingly enjoyable throughout, and Hawkeye and Black Widow have a major plot arc (concurrent with a couple others, plus the Battle of the Week) that gets touched on/advanced frequently in most episodes once you get past the first 1/3 or so "intro and setup" eps of the season.

Because of Plotreasons, they mostly aren't able to interact normally with each other for most of the season, but it's really well done in how Plotreasons also demonstrate the ways that stresses both of them, and you can get a good idea of their normal/prior relationship from that.

There's also all the fanfic (mostly Phil/Clint) spawned from their scene in Thor, which generated a fanon-consensus Hawkeye, which Avengers movie fanfic seems to draw on at least as much as any other canon.

(Edit to fix brokedy italics)

Edited at 2013-01-08 04:42 pm (UTC)