I prefer a 16/44.1 format file (CD, AIFF, WAV, FLAC, ALAC, etc). I do have a universal disk player (CD, DVD-A, SACD) for playing Hi-Rez format disks although I don't own many, but it's nice to know you can play any disc that might come into the house if necessary.
My portable player is an Apple iPod Classic 160 GB which stores 16/44.1 files in Apple Lossless Audio Codec (ALAC) format. I prefer iTunes' file organization features, although I don't use iTunes itself to playback audio (see below).
I don't normally store or play lossy compressed formats. I have a pair of Ultimate Ears in-ear "headphones" that sound awesome with the iPod, but for the most part I use the iPod through speakers in the car.
With a new CD, like many people, I rip it to an external 1 TB Hard Disk for the first play, and rarely is there a second play of the CD itself. Files are converted, if necessary, to ALAC with XLD, an open-source MacOS application essentially identical in feature and function to the WindowsOS's Exact Audio Copy (EAC).
I used to use Max but it hasn't been supported for a few years now. It's an excellent choice if you have an older MacOS computer, including a PowerPC unit, though.
Mostly I upsample with a hardware DAC to 24/96 for playback. If I'm at home playback will be via Audivirana Plus sofware; in the car it's the iPod via a TEAC UD-H01 I've installed with a DIY 9VDC regulated power supply substituting for the supplied 120V->9VDC Switchmode Wall Wart.
A few notes:
AIFF is short for Audio Interchange File Format. Although it's often incorrectly referred to as Apple Interchange File Format, it's actually a cross platform format and the default on pretty much every computer OS in existence prior to about 1990, and stores Pulse Code Modulated (PCM) digital audio data.
Microsoft introduced the WAV format for use on WindowsOS systems beginning with Windows3; it stores Pulse Code Modulated (PCM) digital audio data.
The difference between WAV and AIFF in terms of audio data is zero; they store the exact same PCM files, but there are differences in the accompanying data that describes the format to an audio application. MS has a habit of changing file format data just enough to make files proprietary, and WAV is a perfect example. Sound Quality-wise WAV and AIFF are interchangeable.
FLAC and other lossless audio compression formats like ALAC (which is an Apple-developed format, but has been released as Open Source without any royalty requirements) work the same way that other data compression formats like zip work.
Both have become popular in the last decade or so. There are a number of other lossless audio compression formats but since those two are actively developed and free to use, they are good options.
If absolute minimal file size is important, Monkey's Audio ( .ape ) might be considered, but it's worth mentioning that FLAC and ALAC have improved their compression performance with recent updates so that the files are now only about 5% larger than APE files.
Some wonder how you can compress an audio file without loss of data. A (very) crude explanation is you remove redundancies. For example if the digital data is represented in binary format as:
01100000
You could instead describe the file as:
One 0, two 1's, and five 0's
... and then re-write the data in a way that uses less than the original number of bits and bytes to describe that data.
For playback you reverse the process and thusly the original audio data is available without throwing any data away, to achieve a smaller stored audio file.