What is the preferred method of using iTunes Apple Lossless? MP3? other encoding?

IMHO: Lossless is excellent for high quality earphones, and for playing through a decent stereo. I've no understanding of the other high quality formats (flac?). AAC compression is better than MP3 compression at any given bit rate, but limited to Apple devices as I understand. MP3 is more universal but takes more space for any given level of sound quality. The sound quality jumps are substantial when you go from 128 to, say, 256 or 320. The quality improvement from 320 to lossless is very noticable on a high quality audio system or high quality earphones, but subtle otherwise.
My two cents.
Absolutely, positively Apple Lossless ... don't use anything else. If someone gives you FLAC files, convert them to Apple Lossless using a program called Max.
Using iTunes - ideally on a Mac, since for various reasons iTunes does not seem to perform as well on a PC...

There are two uncompressed formats; WAV and AIFF. An uncompressed format is what comes on your CD. iTunes can handle WAV and AIFF files but there is a better way to go.

That is Apple Lossless. Apple Lossless preserves all of the data in a WAV or AIFF and sounds exactly the same. In fact you can find numerous posts from people who tested that by reconverting Apple Lossless back to WAV or AIFF - the files were identical.

Given that you do not have to compromise on sound quality, there are two things that make Apple Lossless better.

1) Apple Lossless takes about half the hard disk storage space. Meaning that you can get twice as much material on a given size hard drive as you can using WAV or AIFF.

2) Apple Lossless was designed to handle metadata. Metadata is all the information you want to have about each song - album name, song title, artist, time, cd cover etc. Much of this is gathered automatically from the internet when you rip a CD. Without going into detail, WAV and AIFF do a miserable job handling metadata which means that you can not take advantage of many of the reasons people switch to computer audio to begin with.

There are not many secrets to getting a clean rip using Apple Lossless. The main one is to check the box for "error correction" and to make sure that the other boxes are unchecked.

I am not sure what you mean about the best way of using Apple Lossless - just use it when you playback through a DAC. I also use it to load my iPod but if you want to have a bazillion songs on your iPod you can cram even more on there by using a utility that converts Apple Lossless to MP3 which is a compressed file - meaning that it is smaller in size, and that it does not sound as good as an uncompressed file....
Thanks...... I originally loaded about 650 CD's onto hard drive using default settings .. my lack of knowledge at the time. I am going to start replacing them (reloading) using Apple Lossless with error correction to rebuilt the data base in the least compromised manner before moving into Music Server land ..... . If I am saying something that does not make sense to those who know far than me (almost all of you) say so.
How important is checking that error correction box when ripping cds in iTunes? I unchecked it early on because I found that I was getting worse results, but I don't remember the details, sigh... I think it was ripping more slowly and at times giving me strange artifacts in the sound. My memory on this is vague alas.
Pretty important if you want the best rip possible.

It will take longer on dirty discs - if you have some smeared with fingerprints and peanut butter best to wash them (literally) before you rip.
I’ve been using iTunes in my 2nd system (garage) for years and have been happy with it. I’m still in the process of losslessly downloading, using error correction, several hundred more CDs into the iTunes library.  I recently learned of andadded the iTunes Play app giving us the ability to control iTunes through wifi remote control in either location using an phone or iPad. All that had to be added is a digital cable connecting the Mac in the garage to a DAC in the living room. It’s simple, easy to use and these lossless music files sound very good in either setup. BTW, since our wifi is often unavailable I keep a CD transport in the main system still.