There are several ways to approach that concept, so I will share with you my personal experiences.
I bought an HD500 in 2010 to replace an X3Live.
From 2010 until last month, I always used the HD in 'studio direct' mode.
I would use a combination of means to amplify it, sometimes just plugging direct
into a mixer going to PA / monitor speakers.
As far as using a guitar amp with it, I have three solid state amps, which all have fx return 1/4" jacks.
Two older Fenders, from the CBS / Paul Rivera era when he was still with Fender, before they did the big changeover, and a Marshall valvestate, all 1x12's. If I wanted to go stereo, I would use any given two of those amps. With the mixer / PA, same thing, two XLR's to the board.
THEN, in January of this year, I threw down and bought a DT25, followed very shortly after with a JTV.
Using a DT25 is a very different approach to how patches need to be constructed, and adding the JTV furthur altered my thinking. For example, my other main guitar is a HSS USA strat, and the power in my apartment (upstairs apartment in an old 1890's two flat chicago house) is horrible, and always induced nasty hum and noise - so every patch I built used a noise gate first in the chain, on always.
With the JTV going VDI to the HD500, and the HD going L6Link to the DT, it all changed.
Now, I use the "pre" models for all my patches, don't even attempt to run stereo, and use the XLR off the back of the DT25 for the mixer / PA feed, and for recording.
I sort of miss the simplicity of running the studio/direct mode, so for you - for starters, you may want to get your hands on a keyboard amp, or a guitar amp with an fx return, or a powered PA / monitor type speaker with XLR or 1/4" ins. Use the same patches you have built using headphones, make sure the HD is in 'studio/direct', and see what you think of what you hear through actual air as compared to what you are used to hearing in headphones.
It will be different, though it should be close.
The reason I say that, is something like a PA speaker, or a keyboard amp will be 'full range / flat response', so it's not trying to 'shape' your tone the way the front 1/4" jack on a regular guitar amp will do.
In terms of the DT, big investment of $$. The DT25 is a $1,000 amp, and if you want to do dual amps or stereo signals using the L6link, you need two of them. The DT50 just goes up from there in price, same for the head and cab combos. BUT, they are really the most amazing means of letting your amp and your HD tallk to each other.
I prefer to think about the DT amps as "Bogner". The analog tube amp part of the DT is all Bogner; the digital interface, and the Link system is Line6. When your HD changes to a Marshall plexi model, the DT changes itself in the analog / tube / poweramp stages to emulate what a Marshall would be, and if you switch to a Fender, it changes actual relays, switches, and analog components, on the fly.
I am still working with creating new patches, because none of my old patches were set up right to properly utilize what the DT is going to do to your tone.
As it is, with no DT - the HD is going to model the preamp, and the poweramp and the cabinet and the microphone, in order to emulate an amp, a speaker, a room, and a mic. That's the studio/direct.
When you L6link to a DT, it changes the output mode to "combo/poweramp" or "stack/poweramp". This just removes the mic modelling. When you build the patch using the "pre" models, you then also remove the power amp modelling that the HD would normally do, and the DT then does *actual* poweramp changes.
If you can get your hands on a regular guitar amp, with an FX return, try a patch in studio direct, then with the same patch, change the output mode to "combo/poweramp" or "stack/poweramp", but keep the "full" (regular) amp model choice, not the PRE. This just removes the 'room' and 'mic' modelling, which will give you a sound that will work great in the amp, but you would then have to actually mic the amp to send a proper signal to the mixer, recording, etc.
I often would dial up a tone in studio direct, then switch to poweramp/combo in order to 'tweak' the sound of what that amp would be like with no mic. Then when I like it, I switch back to studio/direct, and start tweaking the mic choices, and the mic settings to best represent what I think that amp model should sound like, if it was in a real room with a real mic.
Sorry for the extended rambling response! Most important: HAVE FUN!