From the paint you have exposed the unit doesn't look scratched up, the sticker doesn't look like it is pealing or all nicked up...
I would take care when I pressure wash not to spray any stickers. Honestly I would roll it out back, soak it down with some purple power or simple green real good, use a microfiber towel or soft brush to agitate it rinse, and repeat.
Don't repaint everything unless it is really that bad, original paint and stickers on old stuff is way more cool then new paint and new stickers. Honestly all the oil all over it currently is a blessing because it has preserved everything well from what I can see.
I say clean everything really really good, and maybe paint only the pump. Also if you have automotive paint mixed figure out a way to bring a part with good factory paint on it even if that means loading up the whole tank and bringing it with you. Any person good a mixing paint can match that paint perfect with out the need of a sample or anything. That way your newly rebuilt pump will look like it was never repainted....
One more thing, if you do end up repainting which it is yours so that's up to you. Please don't use rattle cans, rattle can paint is not very good quality it won't last and will be more crappy looking then the paint that is on it. Go to an auto paint supplier and get it mixed, there are cheap lines out there like Nason that are still very good quality paints. If you take my advise and just paint the pump, you can have them mix the paint and put it in spray cans or buy refillable spray cans online, but for large objects such as the tank they won't work very well because the paint will flash to quickly.
Wow my short comment turned into a book, maybe I feel stronger about all of this then I thought
Edit: Also if you do have minor scratches on the tank you could polish them out most likely keeping it original but look new just take your time so you don't wear through the paint.