If the stained woodwork has been varnished you can apply a Zinsser primer without sanding, and then one or two coats of Acrylic primer undercoat and a top coat of your choice, either white spirit based or water based. If there is no varnish you will not need the Zinsser as it is expensive.
A.L. SMITH DECORATORS,ESSEX, Est 1980
With respect to skirting boards, I apply two coats of acrylic undercoat, re-coat when dry, one coat of solvent undercoat can be applied when acrylic coats have dried, and either solvent gloss or satinwood to finish applied next day.
Re your doors, many doors that are stained have a rough finish therefore sanding is required beforehand and the above procedure followed, I would suggest satinwood be applied to doors, more of a sheen finish
Emery Painters Decorators
you need to apply a good undercoat/primer like zinnster that you can get from a trade suppliers.
then i normally give the wood a second undercoat with macpherson trade undercoat before applying a coat of one coat gloss or satinwood.
hope this helps.
kind regards stephen sjp decorating services halifax.