you're on the right path to unprecedented mp3 and ripping quality!
First of all, let me give you some great links: http://www.hydrogenaudio.org
This is Dibrom's site. He made the latest quality improvements to LAME http://www.audiofora.com
This is the forum of the r3mix.net site. R3mix is basically father of the "mp3 quality movement". His site gives info on EAC, LAME and useful utilities around mp3. You should really sign up to this forum, cause that's what got mee started, too.
Ok, now how to use LAME:
There are certain levels of quality that you can set for your mp3 file; basically the higher the quality, the bigger the file.
This is, as the name implies, insane! The resulting mp3 file will be 320 kbps CBR (Constant Bitrate) and makes use of some tweaks to improve sound quality. If you still hear flaws on this one, mp3 will never satisfy you since this is the mp3 format at it's max.
Extremely high quality VBR (Variable Bitrate) mp3 file. Will result in a mp3 file around 230-260 kbps. This is enough for most (even some audiophile people) users, since it handles even extreme sound situations at a good quality.
A standard encoding on a very high level of quality. Definitly smaller than extreme, but I always invest a little more kbps (exteme) just to be sure about quality.
This is just very small amount of the command lines available in lame, but they're very sufficient for your a "newbie" and produce the absolute best mp3 files up to date. If you get more into the topic (you have to read lots of forum posts) you can start tweaking these lines or even create new ones, but stick with them for now, trust me.
Since LAME is a command line utility I recommend you to use a frontend (a nifty Windows UI). The most popular is RazorLame, available right here: http://www.dors.de/razorlame/
You have to configure it (tell it where lame.exe is etc.) and set it to use one of the lines mentioned above. This is all pretty self-explaing and if you found your path to Lame, you'll get into it, I'm sure.
About EAC: You have to configure it properly to let it work it's magic ;-) See this extenisve tutorial page for details: http://www.ping.be/satcp/tutorials.htm
Happy ripping & encoding!
If further questions arise, mail me at firstname.lastname@example.org
or post your questions to the forums mentioned above. Personally, I'd recommend the r3mix.net forum, since these people are just more friendlly to new users, while still maintainig a certain level of knowledge. hydrogenaudio.org is more like a "one-person-cult" and every thread ends up with "Thank you Dibrom! You're so great!" blablabla... his tweaks are great but I dislike his community. But see for yorself...