There are basically three ways to go.
- Record a real amp with microphones - I won't go into detail on this, because it's pretty clear it's not what you want.
- Get the sound right in the pedal(s), and have the PC record that accurately
- Record an unprocessed sound and have the PC apply effects
Taking (2) first:
Your GT-6 does amp modelling, so you have all the equipment you need. First set your GT-6 to a clean sound, and make sure you can record that properly. Check with headphones plugged directly into the GT-6 headphone socket, before working on the link to the PC.
I notice the GT-6 has an S/P DIF digital output, and the Firewire Solo has S/P DIF digital input - so use these instead of the analogue connections, to avoid a step of Digital/Analogue conversion.
If for some reason you really have to use analogue to link your GT-6 to your audio interface, bear in mind that the GT-6 has a stereo output. Things like reverb do make use of the stereo feature, so hook up both stereo channels (e.g. to the stereo line inputs at the back of the Firewire Solo).
Make sure all the input/output levels match up, that nothing is coming in too loud and clipping, or coming in too quiet. This is much easier if you've used S/P DIF - there are no levels to adjust for that link.
In your PC software, treat it like a keyboard input - don't have any effects at all. You might later add small amounts of reverb and EQ.
Once the clean sound is working, get the sound you want by fiddling with the GT-6. Since you don't have a real amp/speaker, turn on the simulations in the GT-6.
Don't use the GT-6. Plug your guitar straight into the "guitar" input on your audio interface. Again, make sure the clean sound is good before trying any distortion. Now you will need software to make it sound good. The software you've mentioned all does what you need: Amplitube, iZotope, Guitar Rig. They simulate the pedals, amp and speaker.
But now you're asking: which is better? Can I mix the two?
(2) has the advantage that you can use the GT-6 sounds and user interface you've got used to. You can use the expression pedal, switch effects mid-song with pedals, etc. It puts less of a load on the computer, since the computer isn't doing the effects work.
(3) has the advantage that you can tweak effects after recording. Most recording software records the unprocessed sound card input, and applies the effects during playback. That means you can change everything about the amp simulation etc. any time after the recording. But it means that the computer is working harder - that sometimes becomes an issue with multiple tracks, where things lag or even can't play at all because the computer can't keep up.
A hybrid approach is possible - in which the GT-6 does some of the FX work, and the computer does some more. But think carefully about this because applying effects in the wrong order can give unwanted results. Think of the order things happen in a traditional pedals + amp setup, and concentrate on simulating that at first. So for example, you could turn off amp/cab simulation in your GT-6, but still use it for flanging/delay/chorus, while letting the PC simulate the amp/cab.
Now, with all the technology sorted out - how do you get your "great metal sound"? That's a separate question; there's no single recipe. Try using the presets in your GT-6 or your software as a starting point. Study which effects they use, in which order; tweak and experiment. Your playing style also affects tone.