The reason you didn't enjoy those headphones is because they're not very good for what you want to listen to. And, to be a broken record yet again, the pricetag does NOT mean something is good. If anything, we're awash in expensive and mediocre (at best) equipment.
I also spent a lot of time as an instrumentalist and find a lot of headphones to get it wrong. If you want something very good on a budget, try the AKG K-501 (as well as earlier iterations, like the 500, and 4XX models), the AKG K-240DF, and the Beyerdynamic DT48. Those get things right and I paid $100 or less for them used. If you want to spend more, the Sennheiser HD-600 and HD-800, AKG K-1000, Grado HP-1000, and various Stax 'phones get things right.
The vast majority of headphones out there are voiced for rock and hiphop, since those are the most popular genres. You'll find the bass overemphasized in most of them. Overdone bass is a big seller and I can't blame the companies for trying to please customers. But a certain segment like us won't be happy with them.
You will need an amp for these headphones. I like to recommend old receivers. You might already have one around the house. If not, thrift stores, Craigslist and garage sales will turn them up cheap. If you can spend a little, get a good solid state amp like a Dynalo. The cheap tube amps might look cool, but many aren't built particularly well and some have questionable transformers. Dollar-for-dollar, solid state is better. Tubes can be remarkably good, but you'll either need to drop a lot of cash on one built right or DIY one. DIY, by the way, is a great option if you are interested.
Don't get hung up on the source myth, either. People confuse iPods and laptops sound quality with their internal amps. An iPod has a relatively weak amp suited for efficient IEMs. That does not mean that the output is bad, just that its amp won't power much.
I'd recommend a standalone CD player. If you have a DVD player handy, it'll be fine. If you want something new, the Sony SCD-CE595 is terrific. Think I got mine for around $60 and it plays SACD. Oppo makes a nice player, too, and there's a $100 Sony Blu-Ray player getting strong reviews.
Skip the pricetag snobbery on sources, as well. Some people think that nothing under $1,000 or so is any good. Nonsense. Digital is good and cheap these days. You can pay a lot for a fancy case - a number of manufacturers have been caught using ordinary consumer players inside a fancy box.
So focus on finding a really good pair of headphones. Those, along with excellent recordings, are about 90% of the equation. An amp is probably close to 10% of the rest. Sources aren't worth worrying over unless you're spinning records, but that's a different rant. Another rant is the cable/tweak nonsense. That stuff does nothing but make money for the people selling it.