I purchased all of my Mesa gear second hand, just like yours it was in great shape but needed a little TLC - at least to be as clean as I wanted it to be.
I used this stuff from Meguiars on just about every amp I have ever owned, it works absolute wonders on tolex, leather, badges, plastic, diamond plate, and that stupid brushed metal look that alot of amps have for a faceplate. It doesn't leave a film or a shine or any other BS. It just cleans. Make sure you get this one, there are many others packaged like it that leave a shine/film etc.
Meguiars Quick Interior Detailer
Just spray it on a microfiber and wipe as if you were detailing your car's dash. I always use your standard run of the mill microfiber towel
Microfiber Towels
If the tolex/leather is really dirty then you might want to use a few of these cleaning wipes from armorall. Again I used these on my own Roadster head and had great results - it had a little white paint on it on the bottom, looked like it picked it up from being set down on some woodwork that was painted white. Paint came right off. Just make sure you wipe this stuff off with a clean rag and then go over it with the quick detailer.
Armorall Cleaning Wipes
You may want to consider taking the amp out of the cabinet too just to make the cabinet easier to clean. Just be careful as you can screw it up bad if you don't take your time and pay attention.
I've never touched the diamondplate with anything other than the quick detailer as I heard it had a film on it that regular metal polish would take off.
Have fun!