Do you mean a typewriter that is new to you? Or one that is a part of your collection?

When I get a new machine that's in rough conditionI always give a cursory cleaning first just to get all the cobwebs and mouse poo out of it, and make it a little more pleasant to work on. Next I test every single function of the typewriter to determine what, if anything, needs repair. After any repairs have been made and the machine is working fairly well I'll do a more detailed cleaning. A really foul machine might need a dunk cleaning first, but otherwise I just work methodically from top to bottom concentrating on the mechanical components first and leaving the trim, paint, and keys for last.

Only after a machine is very clean do I worry about lightly oiling it. I use sewing machine oil, and apply it to the mainspring drum axle, the carriage rails, sub-key assemblies (front and back), the ribbon transport and spool gearing, and the moving parts of the escapement. 

On machines that are in better condition and are working well, I tend to combine maintenence with typing: type a little, clean a little, tinker with or clean anything that I notice needs attention when I'm using the machine. 

I don't really have a method/order for cleaning. I tend to jump around and do whatever suits me at the moment.  Eventually, it all gets done.  Usually, I start with the inside, but I'll often skip back and forth between inside and outside.  Seems like getting the outside clean is a bit of a morale boost and gives me hope that it will look good as well as work well. I should probably be more organized, but I'm doing this for fun, so I do whatever strikes me. Of course, once you've gotten a cover off (a difficult cover, yes, I'm taking to you, Royal Royalite) it makes sense to do all you can to the inside before getting it back on.