Recording 2 sounds is easy. Create 2 MONO AUDIO tracks, set the inputs for your setup and start recording. I would go a bit further and make a group of the 2 tracks right off the bat and add .1 to the track names(so BassDI.1 and BassAmp.1). The reason for that is so if you do several takes on playlists, each time you create a new playlist, they will get named in succession(next Playlist will be BassDI.2 and BassAmp.2 and so on).
As to what DI, it depends a bit on your budget. The Fat Mo' is great but pricey. The Ampeg SVT tube DI is also great and a little less. I used KT's active DI and never had a complaint about from session players over several years. Of course, a Radial JDI is a solid choice(its got a really nice Jensen transformer). This thread will likely see several other recommendations
Then you need a mic on the cabinet, but since that's going to be a gritty sound, you can probably get by with most anything, down to the old "standard" SM-57
You will probably(after recording and comping) need to slide/nudge the DI track a tad later to align with the mic track as they will be slightly offset.
I am also a fan of having both clean and gritty, but I go about it a bit simpler. I track the DI to an AUDIO track and that track has a send feeding a MONO AUX track where I insert IK Multimedia Amplitube SVX. A few tweaks to the amp and add a stompbox overdrive or distortion pedal inside the plugin gives me pretty much the same thing as you(but I don't have to nudge anything)
