Thanks for the responses.
The shop I went to had a Marshall (Micro) Stack. I played a Tele through it, and it was OK. I then played a Les Paul through it - and I was reminded of the old LP through a Marshall thing - it still holds true! Some distant, yet recognizable, derivative tone was there... The one watt of power is plenty sufficient. It fills a room easily. I went with the Marshall. Its a joke, but this joke does the job.
At some point, based on the feedback, I'll have to try a Pignose.