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.
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.