As a newly licensed HAM (since Jan 2015), I'd like to give a few words of encouragement for people thinking about getting US license.
I thought about taking the exam for a LOOOONG time. Things started to move forward when I joined local HAM club, and asked around about the procedure, exams, and all technical details related to getting licensed. It turned out to be much easier than I though. When I checked requirements for Tech license, I decided that it would be a waste of time (trivial exam, I'd just have to study a bit the rules), and I should get the General license instead. However the real kicker that motivated me to wrap up and take a trip to the examination center was ordering a handheld radio. It was a cheap Baofeng, but gave me a strong motivation to move on. After I went through the material for General exam, I still did not feel challenged enough, and I started to study for Extra. My goal was still to get General license, but I decided to take a try with more advanced topics. I went through the entire material in less than a week. The exam session was on Saturday. I went to the examination center in the morning, left after 3-4 hours having passed all 3 exams on the first tries, and on Monday before noon I had callsign assigned by FCC and I could start using my brand new radio.
Turns out that for someone with EE background getting the license should not be difficult. Tech exam is trivial. You will have to study the rules a bit, but I have a friend who passed the exam after reading the ARRL manual once during his flight. General is probably what most people should shoot for, and it's the license which really opens the HF bands, where most of the fun is. If you like the challenge, you can try Extra. You can take all 3 exams on the same day, and you loose nothing if you don't pass, however basic EE knowledge may not be sufficient to be successful.
Regarding studying materials: I found "The no-nosense study guides" written by KB6NU to be very helpful. Electronic versions (PDF) of guides for Tech and General are (were) available for free, if you prefer e-book or printed book, you can buy them from the author. Guide for Extra exam is also available for purchase. These are good books to help to study.
Another useful resource is
http://hamexam.org/ You can go through the entire question pools for all three levels, take practice exams, and check your stats to see what topics you know well enough to pass, and on which you should spend more time studying. Dot try just to memorize what answers to check. You don't have to hurry, so don't guess. If you don't know something, go to google, or open a book, and learn how to answer the question.