questions about streaming source for a headphone amp

I've owned some decent headphones in the past but I want to move up in the headphone world (Clear, 800s, Arya and a suitable amp). Basically, I'm trying to figure out if getting good headphones means building an entirely new system. I've been researching headphones and amps, and when I came up for air I realized I need a suitable source....

In the past I've plugged my headphones (e.g., Sennheiser hd600, Grado RS2e, etc) directly into my phone or laptop or preamp, and it's been fine. I'm guessing, though, that something like the 800s needs a dedicated amp. I'll mostly be streaming music and I'm not especially keen on buying a new streamer and dac as well.

1) Would it make sense to do this, using my current stereo system: streamer > dac > (preamp?) > headphone amp? My preamp has two sets of "outs"; my dac has both balanced and unbalanced outs. I have no idea if I can run cables from either the preamp or dac in two separate directions. I know this is newbie stuff but would I have to turn off my speakers (at the amp or preamp)?

2) I'd like the source to be consistent in quality with the headphones and amp, the whole weakest link thing. I know this gets asked all the time but is an iPhone or MacBook an appropriate hq source for a good heaphone/amp combination? In that case, to stream hi-res, would I use an external dac (Audioquest dragonfly??). It feels a bit strange to me to spend $$$ on a headphone/amp combination and then stream the music from an iPhone via a portable dac. 

I'm interested that there aren't more headphone amp/streamer combinations. The Naim Uniti Atom HE looks cool, but not inexpensive. (The Aurender A30 ... $$$.) 

In short, how do people stream music through a headphone amp? Do you simply have a dedicated streamer and, if necessary, dac? (My son has a bluesound node I could experiment with.) Do you use your phone or laptop through an outboard dac? I'm sure I'm missing all kinds of things here... 

If I’m you, and since you’ve already got all the other necessary equipment, once I choose headphones I’d just buy a good headphone amp that meets your power needs and sonic tastes and run your current DAC’s or preamp’s output into it — done.  Simple is better in my book.  Hope this helps. 
It's pretty common to use headphones with your computer as the source, and I think if you are connected to a high-quality DAC + headphone amplifier there is no reason not to do so. But yes, I think you'll get a lot of benefit by introducing some high-quality electronics into the chain.

To answer your basic question, most people use your computer to an outboard DAC and headphone amp. Some people, but not a whole lot in my experience, use a portable DAC+amp with their mobile phone or tablet.

Usually a streamer is only used if you are separate from any sort of computer. In which case you might use your phone or tablet to control the streamer, which is then connected to a DAC and headphone amp.

Almost all streamers are standalone for use with a DAC, or include a DAC for use with a speaker or headphone system. There are a few products that are truly all-in-one but most have mid-level headphone amplification.

You can use the multiple outputs from your preamp to feed one to your speaker amplifier and one to your headphone amplifier. You will need to manually turn off one of the amplifiers to make sure only headphones or only speakers are used at a time.
$723 for cans.
$299 balanced tube amp.
M O #1
5 streamers <$1K each.
All good.

Thanks to you all for such clear and helpful answers. I'm glad to know that I can run the headphone amp from the preamp or dac--that might be my best solution, though it means that I'm wedded to a single room.

I'm interested in using my MacBook and I'm glad to know that many do so. Does anyone have any obvious ways to bypass the laptop's dac? It looks like I'll need to use a USB connector of some kind ....

Again, thank you!
@northman USB is probably the most common digital connection from a computer to an external DAC or audio interface and what you should use. But older Mac computers also included a mini-TOSLink output in the 1/8" headphone jack.
Owning 'decent' headphones does not translate into experiencing / having 'decent' or great sound quality.

I've owned some decent headphones in the past

In the past I've plugged my headphones (e.g., Sennheiser hd600, Grado RS2e, etc) directly into my phone or laptop and it's been fine.

To get a handle on whether "it's fine" purchase an Audioquest Dragonfly Cobalt or Red, connect it to your MacBook (you may need a connection dongle, depending on your MacBook version) , and connect your headphones to the Dragonfly. You may need to select your audio output. Mostly plug and play.

Consider this a starting point. There are many options and paths to move forward with. The return / rewards are significant.

Experience a taste of what's possible. Then choose your next steps.

All the best. - David.

+1 re @nekoaudio  's posts.
If this is for a desktop setup, then all you need is a USB DAC + headphone amp.

JDS Labs makes great performing gear (Atom+ amp and DAC) for a reasonable amount of money.

Currently I use a Benchmark DAC3 HGC with my PC and use foobar2000 to play tracks from a shared folder on a Mac mini. Works really well.

Hope this gives you some good ideas.
I'm interested in using my MacBook and I'm glad to know that many do so. Does anyone have any obvious ways to bypass the laptop's dac? It looks like I'll need to use a USB connector of some kind ....
Yeah, it’s just that a laptop is a noisy music source that significantly affects the digital signal.  I’d get an Apple USB 3 adapter that bypasses the MacBook’s DAC and gives you a USB connection, and into that I’d plug an iFi iPurify3 that’ll largely clean up the noisy signal.  Then it’s a matter of choosing your headphones and the appropriate headphone amp/DAC and you’re good to go in any room.  I have a Dragonfly Red that does work well, but that’s not powerful enough to get the best out of the headphones you’re considering although it may still be viable if you need/want to go truly portable at some point.  Hope this helps.