Dear IonicRage,
From my personal experience nothing beats testing the gear yourself.
First thing, Id like to share with you two forum psts that I belive are very usefull:
http://www.head-fi.org/t/634201/battle-of-the-flagships-58-headphones-compared-update-audeze-lcd-2-revision-2-6-4-13
http://www.head-fi.org/t/534479/mad-lust-envys-headphone-gaming-guide-update-7-9-2014-ultrasone-hfi-15g-added
I suggest you read all the information from the first post to get a very good general Idea of what money CAN buy, and what you actually want to spend.
About AMPs: An amp helps. Unless we talk about an in-ear model, or a very cheap/overpriced headphone, an amp always helps.
Know what amp you want/need is they tricky part.
Personally I use a HE-400 headphone (350 dollars give or take) and a Schiit Asgard Amp (250 dollars). You can however get a great setup buy getting something like the Magni at 99 dollars and a HD600 sennheiser at 299 dollars.
The problem here is that there are so many different combinations and price gaps that it becomes almost insane to try to suggest something without knowing your sonical preferences.
You mention Bass. First thing we need to diferenciate: bass QUALITY and bass QUANTITY.
I favour Quality vs quantity (quality means that instead of sounding like a distorted bass, its very controlled and clean. In fact, its a bass that is hardly Intrusive for other sounds). Quality Bass is usually best in planar magnetic headphones (with a few exceptions). Thats why i bought the HE-400.
In terms of isolation and sound quality, you are in a bad spot: Bose QC 15 are not "the best" isolation headphones, but to get a CLEAR increase in sound quality, and also have isolation, you are going to have to get something far more expensive. I assume fostex TH-600...
If closed cans are a must, I am afraid I cant give you much good info (I favour Open headphones, even when outdoors over closed cans, for isolation I use in-ears).
In terms of Ohms, you also have to look at efficiency. Some headphones are very efficient, even if they have high Ohm resistance. I dont know the exact mathematical formula, so I cant help you there, but im sure you can google specific models.
Please let me know if you have any specific questions.
EDIT:
In terms of audio quality, headphone is about 70% of the quality, amp around 20%, DAC 9%, and the 1% remaining is mostly power distortion, and similar.
(assuming quality of the music format is good).