Since you already have the phonograph preamp, a USB Audio Interface with line-level inputs and a Direct Monitoring switch might be a good option, I believe this would allow you to plug your preamp in and listen with your headphones, disabling would allow you to listen to your computer, as well as to record your vinyl when you're ready to do that too. (I found this thread talking about some of the specifics for one particular setup, might give a general idea). There are a lot of audio interfaces between 50-150, probably at least a few options with that combination of features.
 
Something like that to use at home, combined with a cheaper DAP like the x1 or m3, ipod nano could probaby keep you on-budget...
 
If you can do without the recording functionality, There are also a lot of portable and desktop amps in that price range.... with m50x and x3ii might even be able to squeeeze in just an amp... something From SMSL, Topping, JDS CMOY, even the little $28 fiio e6 could probably give you headphone out from your phono preamp.
 
The e17k dudelw mentioned would give you usb dac function with compatable computer & phone, as well as act as headamp for your phono preamp, no recording though... could still get a little dap like fiio x1, m3, xduoo x2 or sansa clip for avoiding the cell phone and stay in budget.
 
Agree that you can save quite a bit with used gear too.

Is it safe to assume that an X1 and an E17k would sound considerably better/louder than an unamped x3II. That would also solve the vinyl issue as well because I could run my turntable straight to the amp.

badam said:

Is it safe to assume that an X1 and an E17k would sound considerably better/louder than an unamped x3II. That would also solve the vinyl issue as well because I could run my turntable straight to the amp.

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Why assume when you can look at specs
e17k has same output into 32 ohms as x3ii (200mW) so I think not?
for loudness e17k does have a higher max gain setting (12db) vs x3ii (8.3) (does not make it better at driving, since output is same I think).
Not that m50x and other cans mentioned need a ton of power to sound decent.
(as mentioned above there are a lot of affordable headphone amp options you could get for turntable)

Keeping it short:
 
Portable headphones in general are easily driven by DAPs (Digital Audio players) without the need for an external amp.
 
A simple desktop amp should be sufficient for connecting your pre-amped turntable to the headphones. So the connection would be: turntable>pre-amp>headphone amp>headphones
 
The audio of your computer depends a lot on which sound card you have. Using a DAC will usually give you an improvement, but this improvement will certainly not be as significant as purchasing better headphones with the same budget.

Maybe change the M50Xs for the MSR7?

So it's seeming like the x1 is a considerably better choice for me and that would free up some cash for an amp. I'm looking hard at the Magni 2 its seems to be a lot of bang for your buck and very well reviewed. I also like that it is RCA input so I wouldn't need any adapters. Now if I could only figure out what cans to get. This gets harder and harder with every suggestion.

badam said:

  So it's seeming like the x1 is a considerably better choice for me and that would free up some cash for an amp. I'm looking hard at the Magni 2 its seems to be a lot of bang for your buck and very well reviewed. I also like that it is RCA input so I wouldn't need any adapters. Now if I could only figure out what cans to get. This gets harder and harder with every suggestion.

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That's the hard part  If you order direct from Schiit, magni only 99 vs 130 or something on amazon. On another thread someone recently recommended Bravo Audio Ocean amp as a starter, might be worth a look if you like the idea of a tubeamp.

So bringing up tubes brought me back to the Monoprice hybrid tube amp. Right now I'm using an old JVC cd player with only aux line in. It gets the job done but I think this would be better and it has a headphone jack. Any thoughts on the Monoprice versus the magni or that bravo ocean? It would put me a little over budget but hey I ain't too mad about it.

That monoprice looks kinda cool. Hopefully someone can chime in, if not sure there are some threads on here about those items. Schiit also makes a hybrid tube amp called the Vali.