Can someone help me decide between an amp and an integrated amp?

@bradkava,
If you want to save space and possibly some money buy a good integrated amp with enough power to drive Maggies. With an integrated amp, you don't need to purchase interconnects for a preamp.
If you have space and funds then individual components are an option.
It's a matter of personal choice and no one but you knows what your preference is. I also should mention that I believe in the long run it's worth waiting in order to purchase components that are really good vs mediocre.
For example, this would do the job nicely: https://www.audiogon.com/listings/lis9die5-luxman-505ux-mk-1-integrated-amp-solid-state
I'm sorry to say I don't know if using your headphone amp would work as a preamp. I think we would need to know the specifics of the headphone amp. It would also be helpful to know a dollar amount you are willing to spend.

Hi not sure which Maggie's you intend to purchase and have no experience with the amps you mentioned but I did use a Parasound integrated with 1.7i and the sound was amazing.
I guess separates or integiverated just depends on the best available deal. Just be sure you have enough current to drive Maggies.

That Classe is a really nice piece for the money. 

Maggies, huh? Put Bryston on that list, be surprised how many maggie owners prefer Bryston. Should be able to find something used close to your budget, but a few more $$$.