Help with LP-to-Computer recording?

What a great forum, I just discovered this tonight and have been doing some surfing and reading various posts, and have a question I haven't found an answer to.

Sorry for the long post, but I'm hoping someone out there will sympathize and recognize my problem and perhaps have a solution.

I want to record my old LPs with the goal of putting all of them on my iPod, and some of them (additionally) onto CD. I bought the TEAC GF-350, which is a turntable and CD recorder in one bundle with built-in speakers (and AM/FM tuner, oddly enough) but the quality of the recorded CDs is horrible, and the equipment is very poorly made. Though it works for recording CDs, the tone was so bad I finally stopped making them. I then ordered an 'ION USB Turntable' for which I waited 6 weeks (from Amazon). It comes with USB cable and Audacity software, all of which is supposed to make it so easy 'even Grandpa can record his old Big Band LPs onto his computer'. Though I'm 54 and DO have some Big Band albums, I'm fairly up on computer use, but found Audacity software beyond my grasp. I finally decided to use my old Technics turntable (a perfectly servicable unit); bought a phono pre-amp and cable and have been able to run my turntable into the computer and play music. So far, so good...now I just need some guidance in finding a TRULY SIMPLE software for recording my LPs. I can either save them as WAV files, or better yet, find a software that will save them as MP3s (from which I HOPE I can get them onto my iPod, correct?) The latest software I loaded (Creative MediaSource Player) seems to be something I can handle, but though it appears to be recording as I play an LP, when I click on the icon (I save songs to the desktop) it plays just for a split second, like a 'pop'. I don't even need cleaning or editing software, I'd be happy to record my albums just as they are (aside from manually inserting track changes and titles, which I think you have to do with all software).
Thanks for any help anyone can offer.

Thanks, Robert for taking the time to make this response. I'll check it out.

Hey, Steverm2,
Thanks so much for the response. I'll see if I can hunt it down. You didn't mention price, I'll do a search for it.
Matt

Thanks, Steve,
I located his website online last night and purchased the 3-part suite, including the wave editor, equalizer, and track stalker. Haven't tried them yet, but Drew, the guy who runs the DAK site (and whom I assume gives his initials to the name of the company) is somehow affiliated with The Limelighters, one of my favorite old folk groups (same genre as Kingston Trio and Christy Minstrels) and I grew up listening to my dad's albums. Thanks again for the tip, looks like exactly what I've been looking for.
Matt

Thanks, Ken,
Looks like this software suite I bought from DAK is going to work for me. I just need time to play around with it.
Matt

Thanks, avstooge, I sent Drew a general message and was assigned to Dan also. Though I've only just started to try the software, I sure got a great feeling from this company. Very personalized and really seem to care about the customer, and I'm pretty loyal to companies like that these days. The little time I've had so far has been spent trying to learn the 'track tracker' software for dividing album sides into individual tracks. I'm sure it'll get easier with practice. Thanks for the tip about the equalizer. The truth is, though, that I probably wouldn't know the difference if the channels were flipped, unless you're saying that modifications you were making to one channel were actually being applied to the opposite channel, which I can see would be a problem.
Matt