I'm in the 3-suit max camp... this way you can have one out for cleaning (if necessary) without risk of not having something to wear. For anything 1-week or less, 2 should be plenty and (likely) not require cleaning.

I had enough bad experiences with checked bags, both domestic and international, in a very short period of time a few years back that it pushed me to carry-on only for almost any length of trip. If you're flying to/from Europe on a US-based carrier, a 20" carry-on with a tri-fold garment bag on top should do you just fine, especially if you carry a compact laptop that can go in the front pocket of either bag (United might get dicey if they start enforcing the new sizers). For 1-week trips and 2 suits, an upgright rolling garment bag (B&R U175/U475, for example) along with a laptop bag or something like a Tom Bihn Tri-Star should work fine as well.

If you decide to check a bag, I would recommend wearing one suit jacket, dress shirt, and dress shoes along with jeans while traveling and have the matching suit pants and a tie in your carry-on. This will save when (probably not if) you eventually arrive at your destination and your luggage does not... you might need to give it all a quick press, but you'll be able to do business the next day when you wouldn't if all of your business attire was in a checked bag. This approach saved me on at least two occasions (the same two occasions that pushed me towards carry-on only).