Hardwood is nice, & if treated correctly from the beginning will last much much longer, although softwood if exterior graded, will be just as good if treated in the same manner.
We must try & define Painting as obviously we imagine if it's a soft wood: Knot, Prime and Fill, Minimum 2 udercoats, then top coat too finish.
As previously mentioned you can complete this job all in Oil based Paints but the Final too oat is the tricky one !! It will have too be Micro Pourous paint too allow the timber too breath, i.e. Allow moisture in and out naturally. The biggest problem I see here is that people do spend a lot of time preparing their existing shutters rite back too bare timber all nice and smooth and apply numourous coats of the top coat, no primer, no undercoat, this completely seals the timber and looks brilliant for one summer.
Your seriously would be better off if available here too use Sadolin Oil based they do a huge range of colours I'm sure admin will tell you it can be shipped out if not in any shelfs here but it's brilliant fantastic product along with Sikkens slightly more expensive again. But excellent products that I have personally used for almost 40 years.
Hope this helps but go for the Sadolin, & when the sun bleaches the colour out of them which it will in time at least you won't have a massive amount of preparation too recoat them generally just a dust off wipe down and apply another coat, these products penetrate the timber bit seal it which allows the timber too breath naturally, whether it's a Hardwood or Softwood.