Bingo.
The stock tones actually cover a pretty broad range of classic amp styles. You have a couple Fender cleans that take stomp boxes pretty well and allow you to build some good tones. The J-800 does a killer Marshall sound. The Orange, Recto, Vox and Soldano are all capable and have their uses too. A tube screamer paired with any of those models should get you pretty far.
My biggest issue seems to be finding the right amount of distortion. I've noticed what may feel good for playing usually sounds like crap recorded. But if I cut back on distortion it may not "feel" right while playing but provides a much better recording.