Can't beat a good dip n strip in my eyes.Probably cost you less than £20.Saves a lot of time.And you can ensure there's no surprises lurking under the paint.Plus the inside of the frame gets a good rinse too.Also gives the smoothest finish of course.Unless you want to spend time rubbing down coats of primer filler to even the surface up where the original paint is damaged..Nothing shows imperfections better than a shiny new coat of paint!
And you don't really want too much thickness of paint on a frame,If it's already painted you could be doubling up.Too thick will crack,not to mention paint is weight!
As mentioned,etch primer on bare metal,primer filler after that if you have any rough surfaces you wish to smooth over.
Toughest finish that covers/looks the best is basecoat and lacquer.The basecoat will cover more easily than topcoat.Topcoat is a combination of basecoat and lacquer so is 'thinner'.Lacquer is the toughest of the three layers,so a coat of clear is gonna be harder wearing than a coat of topcoat.
Also,using basecoat and lacquer gives a superior finish to the colour.And is shinier.The more lacquer,the deeper the colour.Really comes alive.Topcoat can look a bit flat.Difficult to explain.
I use a local auto paint suppliers,pick from an endless range of colours,or they can scan colour to find a match.Mixed to order,the aerosols spray really nicely.They'll tell you what colour primer to use too,can make a difference with some colours.Bout £14 for 400ml.Can get 100ml/250ml touch up pots also.
All the work is in the prep of course.Surprising how even a fingerprint can show through paint.Good rinse/wipe over (I use brake cleaner).I normally get two,sometimes three coats on at a time (a few mins apart,before the last coat has fully dried). If you want a real nice,smooth as factory finish,gently wet flat with some 800 grit wet n dry after each layer (once fully dried).Wipe down afterwards,dry,and paint the next layer.The paint will adhere very well and you'll notice how smoothly it goes on.
If you're going to treat the inside of the frame with anti-corrosive/lube spray,best wait till it's painted to avoid contamination!
Bit of a long winded answer but hopefully something of use in there.Hope it goes well whatever you decide!