I've done pretty much this trip ten or twelve times, I've tried most of the possible routes, certainly all the ones listed here, but the one last year was the best. I prefer P & O ferries, but Calais, through Belgium to Luxembourg dull but quick and easy, through Germany, lots of choices of route all quite similar, but we usually go Saarbrücken, Karlsruhe, Stuttgart, Ulm, Kempten and over the Alps to Innsbruck, then the Brenner Pass to Bolzano, the Brenner autobahn is toll, but the old road is almost traffic-free and more scenic, and you're almost at Garda. You'll have to get a Vignette at the border to use Austrian Autobahns, about €10 for 10 days, but otherwise all those roads apart from the Brenner autobahn are free, so much cheaper than going through France. An alternative if you have the time is to head up the Inn Valley from Innsbruck to Wörgl, then off through Zell am See and over the Grossglocknerstrasse, a €30 toll, but absolutely fantastic, wonderful views, just about the best driving road in Europe, and a small motorsport museum at the summit, though only photos of pre-WW2 hillclimbs, just pray for good weather to get the most benefit. After that, head for Bolzano and Garda again, it's further but we were going onto Venice, and not too far out of your way to Garda.
On driving on the wrong side, best advice is to take your time and don't panic, most of the locals are friendly, in northern Italy I'm pretty sure that it's the law to use dipped heads all the time, even on minor roads, I got stopped a year or two ago, but just got a friendly warning, though the fact I was driving a 159 probably helped. One bit of advice I was given years ago was never to drive along the centre of empty minor roads, we all do it, but if you see something coming towards you at the last moment, instinct will make you swerve to the left. I've had that done to me by a foreigner here in the UK, so always drive on the right side of the road, even if there isn't another car anywhere in sight. Have a good trip, and try to go over the Stelvio Pass on the return journey, it's a poor road, but the views make it worthwhile, and no toll on that one.