Looking at the prices on Amazon US, the Trilogy is currently $22 then you'd need to buy Eye of the North (around $20). That will give you the best way to get your HoM points. Each stand-alone game runs at pretty much the same price for each individual chapter. No idea if this is your local currency or not (it's not mine!) I usually just talk in dollar terms when there's no specifics.
If you can get the Complete Collection (trilogy and eotn combined) then this usually runs cheaper than Trilogy+eotn. While I understand only wanting to cash out on just one campaign, you're really shooting yourself in the foot in terms of best way to get HoM points, best way to enjoy the game, best way to be effective etc.
The wiki page on HoM Points (
http://wiki.guildwars.com/wiki/Guide...uments_rewards ) indicates you can get the most points from Nightfall, but that doesn't mean you'll get these overnight, a lot of them are best obtained with the other 2 campaigns attached to your account.
As for which class will get you through a chapter fastest? It all depends on which class you play best at. If you're used to frontline characters, then picking a backline healing monk wont be quick or efficient for you. I strongly recommend having a play about with various classes until you find a style you like. Or if you don't have time for that, watching some Youtube vids to see how the classes play. It's far from perfect, but it's something.
Remember there's 6 years of content here. Of course it wont take you 6 years to play through it all, but there isn't really an easy way to pick up one game and hit the ground running.