Where to start... Maybe I should define "clipping" first; I fear you might misunderstand what I'm saying about that. The clipping that I'm talking about is when someone turns up the volume beyond the capacity of the amplifier's power supply. The input waveform is nice and curvy and sinuous, but when the amplifier runs out of volts that waveform gets its top "clipped" off, distorting it and generating unpleasant harsh noises as a result. Clipping is always something that amplifiers do, not CDs or vinyl records.
When you get into the digital domain, it's the other way around--you want a digital waveform to be nice and square so that every last bit can be read properly. So there are clipper circuits that are desirable, but those I'm not talking about.
No matter how your music is stored, when it gets to the place where it moves a speaker cone, you want the waveform to be as close to identical to the original as possible. There are many exceptions to this rule, but for the sake of simplicity I'm going to ignore them.
If you've ever looked at a vinyl record under a microscope, you'll see the audio waveform in the grooves--that's what "analogue" means, that the music is stored and transported as something that's analogous to the vibrations in the air that was recorded. The analogue recording process is very careful to preserve that waveform at any cost. Unfortunately the end user doesn't have the same budget for electronics gear that the producers of the music have, and that is where most things go awry.
CD digital audio is a different way of storing music that turns the waveform into a bunch of numbers. Your CD player reads those numbers and restores them to the original waveform. In the interest of brevity I'll simply say "trust me, it really works". You're not likely to get clipping distortion anywhere near the CD or the CD player, presuming that it's functioning properly of course.
OTOH I see that you've been buying used equipment that can be fairly old. In that case you may be buying electronics that have bad capacitors. While most solid state parts rarely fail, capacitors are the weak link, and its possible that you've been buying gear that has already begun to fail. After 10-15 years things get dicey. That's why I suggested that you buy a new portable CD player as these cost very little new. If you buy this one critical component new, you have some assurance that it will not be the weak link in the chain. Since there are mechanical bits inside, that's one more thing that can wear out and go bad with age.
You can use your computer to play music! Just don't count on the analogue output jacks to give good fidelity because the analogue circuits inside the computer tend to pick up junk from the digital circuits. You can try using it to drive powered speakers or headphones; perhaps it will be OK. If not, a USB DAC will move the analogue part outside the computer, and give you improved circuits as well. The "you get what you pay for" maxim does apply if you're buying budget parts. You may need to try a couple different brands and models before you find one that sounds good enough to keep, so make sure that you can return before you buy!
If you prefer headphones, that's great! Especially for your budget. I use both loudspeakers and headphones. In my living room I use speakers with my TV and the computer that I play music from. In my bedroom I have another computer, an old Lucid DAC and power amp (Crown "Amcron" D-75) that drives Audio-Technica ATH-M50. If you like to listen to loud music and strong bass, these will do it! When I travel I use cheap Koss earbuds (~US$15) that sound pretty good. Another advantage to earbuds is that they need less power than full size headphones.
This is probably a good time to note that warped voice coils in headphones or loudspeakers can also make distortion that can sound a lot like amplifier clipping. If you get a strident, scratchy sound no matter what level, you should borrow another set of headphones that you know sound right, just to see if yours are the problem. Troubleshooting means checking every link in the chain, and eliminating all suspects one by one.
You make a good point about manufacturers making their CD gear sound worse to boost sales of new gear. However I can't imagine it being a total conspiracy. you may need to shop around, read reviews and even buy and return before you find the best unit. You'll not be popular with the shopkeeper, but the only "sure thing" alternative is to spend lots of money, so...
How is the sound of your Ipod Touch? I have a COWON X5 that I bought in part because it has a good headphone amp.
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