Tinning means putting solder on anything- iron tip, parts to be soldered, whatever. Once a tip has been tinned, it will probably retain the solder for quite awhile, and does not normally need to be retinned every session unless you get it really cruddy.
As far as flux is concerned, ordinarily folks recommend acid flux. I do NOT recommend that for model work where you are working with fresh, clean brass. Brass solders very easily, rosin core flux is perfectly adequate. You can get very fine rosin core electrical solder in 060, even thinner spools.
The problem with acid core is that if you do not wash out the joint after soldering, and get ALL the acid flux out, it will cause paint in that area to degrade. So my philosophy is, never use acid core flux if you can avoid it. Sometimes soldering some stainless (like music wire) does require acid core, but brass or copper certainly don't.