So how good an amp do I need? And will it fix the timing issues I hear? I don't know why the timing might be off as i don't know much about how these things work, but if it hasn't been directly distorted it might be just a function of having poor attack and delay times. Would a poor amp have worse attack and delay for certain frequencies perhaps?
Poor attack and delay times cannot be fixed, get a good set of cans. Delays as in echo cannot possibly occur in headphones, phase delays can, Keep in mind that over half the stuff you read is a load of BS, I hate to say it but most people parrot stuff they've read without either understanding it or having experienced it themselves. Try to find reviews by reputable people that know their stuff, like Tyll Tertsens at InnerFidelity. Buy good cans, otherwise you're just setting your money on fire. Save up what you can and buy the best headphones that you can that fits your desired sound profile.
Also keep in mind this is a hobby so people fiddle around rolling tubes and playing with wires because they enjoy it. Most of this is a fun actvity that alters the sound, I say get a set of cans that sounds right instead of fiddling. As an engineer that has sucessfully designed analog hardware that has sold worldwide, I can tell you that most of what I read by
laymen experts is quite amusing.
In my opinion:
Once you've selected the cans that interest you, do your best to personally listen to them. If you can compare them side by side, that's even better. Bring your own music, that you are familiar with, In store setups, like at Bestbuy, have selected music and electronics that drive them that are designed to trick the basic consumer into parting with their money. A proper establishment has the proper amplification. Otherwise buy from places that have return policies that are without conditions so that you can return what doesn't sound good to you, Beware of stocking and shipping fees, some of which is reasonable.
Learn what to listen for, especially in the music you have. Does the bass extend all the way down and can you discern individual notes (pitches)? Can you accurately hear the clink, clang and shimmer of cymbals, etc. Are voices clear and proper, without annoying silabances? Do percussion instruments and drums snap at you? There's plenty more to listen for my friend. So as I said, "There's plenty to listen for," but I think recognizing this as a matter of habit contributes to the enjoyment of listening to music.
Once you've got the cans sorted out, you have to determine what kind of amplification you need. This is a huge problem when reading all of the BS. There are a few headphones that require special amplification, i.e., some power hungry Planar Magnetics, Electrostatics.
In most cases a good amp has the following attributes:
1) Low steady state distortion, THD, IM
2) Low transient distortion TIMD
3) Flat frequency response
4) Enough power (current and voltage) to drive your cans at their rated impedance and across their impedance curve.
5) Slew Rate, this almost never specified, but if the response is flat to 20 Khz and the transient distortion is low, you are good to go. Chances are you will not be able to make sense of this spec,
For most cans a desktop amp like a Schitt Magni will do a great job and costs a mere $100. Some people get enjoyment fiddleing with tube amps and rolling tubes. IMO this is a hobbyist pleasure designed to alter sound. Since I don't believe in coloring sound, other than some careful bass boost by EQ because with headphones you cannot feel the sound, I would stay far away from exotic expensive amps. I might get flamed on this, however, IMO most of this is BS and if you read the posts you will find conflicting as well as various parroted opinions.
Cables, IMO unless you've got a defective cable or something is wrong with it, stock is just fine. Silver cables have no scientific reason to have any perceptible difference with copper, some people will swear to it, I say that it's just imagination at work.
There is much to learn, technically. There is much to learn as how to listen and what to listen for.
So as I stated, these are my opinions, anyone else is free to have their own, so flaming is not required.