I'm kinda in your same situation. Only that my options are the D2X, Titanium HD and Essence STX. And when it comes to headphones, I'm looking mainly at the Sony MDR-1R and the AKG K550 (has to be a closed headphone, otherwise my gf is going to annoy me because of sound leakage).
While the ST/STX has a built in amp that is quiet good, it isn't as good for low impedance headphones (HD 598, Audio Technica, MDR-1R and so on). The same goes for the Titanium HD. Now, from my research it seems that it would be better to get a D2X (very good dac) and combine it with an external amp like the Schiit Magni. Low impedance headphones will sound better than on the ST/STX/Titanium HD and seen that you can get the D2X for a very good price, it should fit your $ 150 budget....and that is including the Magni.
now i did some research .. the whole thing is gonna cost me a lot more than my budget .. could you tell me why amps in titanium hd and stx are not good for low impedance ... sorry i'm a little bit noob