Almost everything sounds better with an amp and the P51 is a stellar choice. Keep in mind that when everyone says "it depends" they arn't saying "don't buy the T51 or the P51", or anything for that matter, they are just saying that the best choice is your choice. If you have the means, then buy something that's well received by the community (the P51 for example) it will blow you away(go head-fi). But don't let your voyage end there, trade your amp for equal-value amps in the FT forum, you woun't loose money and you will develop a prefrence. I'd say buy the amp first, Iphones don't sound egregious, and FIND OUT IF THERE ARE MEETS IN YOUR AREA, you will be able to try stuff you havn't bought, which is a dream.
So, don't get thwarted by the "it depends on your prefrence" kind of people, they arn't trying to talk you out of that P51, just jump in there and hit that "buy now" button, we all did it and now it's your turn. I shy away from recommending a DAP because you already have one, even though it's made by apple, and those Denon headphones will come to life if you give them the power. Goodluck!