Yea you're not going to want to plug your power amp into your computer's sound card.
Simply take the power amp out of the equation. Your signal chain should be:
Guitar > Multi FX > Mesa Pre > Computer via soundcard > Cab/Amp sim program > Recording program.
You have two options here. You can go with a cab sim PROGRAM which will be less expensive, or an outboard unit like the Pod or Digitech RP500, which are all-in-one solutions. But considering the gear you DO have and the fact that it's excellent quality stuff, I'd go with a cab sim program. You definitely need to keep that Mesa pre in the loop.
You don't have to worry about compatibility with the cab sim programs, as they just act like a plugin that colors any audio coming into it. You can even get cab sim VST plugins that you can use right inside your music program and apply it to any particular tracks of recorded material and tweak at will. This is usually a better solution because you're not stuck with what you've recorded if you decide, later down the line, that you want to change cab tones.
One other thing I want to bring up is, since you're building a rig and you seem serious about this, you absolutely need to make sure you've got a good RECORDING soundcard, not that crap Realtek onboard 16 bit stuff, and not even a 24 bit Soundblaster.
You would be FAR better off with a standard 24 bit external USB sound card (also called audio interface) that features a guitar input and mic input with decent preamps built in.
The AD converters in recording sound cards are FAR superior to gaming sound cards and other general application cards. There IS a huge quality difference.
If you don't have something like this, you should really check what's out there. It's relatively cheap for a basic recording sound card, like the Mbox. MAudio puts out a lot of affordable boxes and they're known for their quality.
If you need any help with selecting an audio interface, or anything else, don't hesitate to ask.
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