What should I do before re-painting my skirting boards?
If you want the boards to look brand spanking new again, you will want to go with method one. I'd use a heat gun to do it, and not the harsh chemical strippers. Either method takes about as long as the other and the heat gun method is less toxic, and, you either already have a heat gun and don't need to spend money, or you'll buy one and have it for a long time - they come in handy. You'll want a good organic vapor respirator for either method still, and a variety of scraping tools.  

Method two sounds more appropriate if perfection is not important. Going this route, you'll want to start with various putty knives and scrapers and knock off any obviously loose and flaky paint, and then use 120 grit sand paper not to remove all the paint, but only to rough up the surface of any remaining paint that is sound and knock down any really high spots. This will leave you with patches of bare wood, and patches of sound, old paint. I don't recommend trying to sand off all of the old paint. If this is your goal, then go with method one. Also - buy expensive sand paper. Cheap sandpaper is a false economy as you'll burn through it so much faster than the good stuff. 

Either way, you should use primer whenever painting bare wood, or a combination of bare wood and sound paint. You don't need primer when only painting over sound old paint.