Flight Search: I recommend using
Hipmunk, as it uses the
ITAMatrix search function. The good part about Hipmunk is that it works like an online
travel agency search (Orbitz, Expedia, etc), but is much more robust. Also, Hipmunk is
not a
travel agent. Their links are directly to the airline's website, which is the best place to buy tickets in case of issues.
As for Delta vs United, there are advantages to both. Delta has better customers service (by far) than United, so your experience at the airport and aboard the aircraft will be better. Plus, many Delta flights have satellite TV aboard (no guarantee, though). In addition, they are pretty reliable in their departure and arrival times. On the downside, Delta has a tendency to switch aircraft and move their schedules around a bit (Delta has a policy if the schedule change was more than an hour, you can change your flights for free to anyone available. As such, you might be able to pick better flights than those purchased). Also, their frequent flier program (Sky Miles) has some of the worst redemption costs if you build up enough points.
United has one of the best frequent flier programs, with excellent redemption potential for future flights. Also, they are in the Star Alliance, which means you can instead credit your flights to
Aegean airline (the Greek airline) and attain Star Alliance silver status with only 3,000 miles flown for (pretty much) life. Status is important, as it gets you
Premier Access (priority boarding (great for carry-on bags), priority security lanes, priority baggage, and check-in) as well as priority customer service lines (great for weather and mechanical issues).
However on the downside, United is working on their customer service (their Fly the Friendly Skies adds talk about everything but people friendly

). Also, they seem to have delays, mechanical, and pilot rest issues more than the norm.
In the end, I generally choose Delta, as I prefer good customer service, but having even Silver status in Star Alliance for (almost) life is a nice benefit to attain from just one round trip.
As for finding flight prices, Hipmunk or the ITAMatrix sites are the best, and it is what the professional miles & points bloggers use.
Good luck and have fun!