How bad is surface rust?

I have a newly acquired casati frame that has some surface rust:

• on the chromed lugs
  
• where there are small paint chips
  
• on the chromed forks
  
  

There is also seems to be a little rust when I look in the seat post and head post. grrrr

My problem is that I love the paint job, a marbled purple, which is quite unique. Should I follow the route of using the jelly rust remover and grease spray inside? And should I do the bath/strip thing mentioned above? Where could I have this done?

Thanks
Matt