If you can get all your clothing and toiletries into a single piece of luggage, then that is definitely the best way to go. It will make it much easier taking a single bag onto the trains and buses and just walking down the street to your hotel.
On my first trip to Europe, I brought a large wheeled checked bag, a smaller wheeled carry-on bag and a computer bag. I lugged this combo through Sweden, Finland, Denmark and Ireland. I dragged them up the stairs to the trains and had trouble fitting them on the buses. I carried them for long distances to and from hotels and was generally miserable. The guy that I was traveling with had a single carry-on bag and not only was his traveling much more enjoyable than mine, but he looked like a local wherever we went and I looked like a tourist.
Luggage was the toughest thing for me in planning this vacation, because I love all kinds of bags and wanted the perfect bag. I always travel with a 19" carry-on wheeled bag for short business trips in the US and abroad. For this trip I decided on a 21" carry-on that did not have wheels, but had hidden pack straps (that I have never used since getting the bag). Behind my choice was advice from Rick Steves because that is what he uses. A wheel-less bag is also much lighter and more amorphous so it can fit more stuff. In fact I purchased a Rick Steves bag on-line from JCPenney that had better prices than the Rick Steves web site. I did not like the fact that the inside was too dark to see things in the bag and the material was too flimsy so the bag would fall flat when opened and all my stuff would spill out. I ended up with a more expensive Patagonia MLC bag from ebags.
My wife needed a larger bag, so she got a very tough and lightweight Swiss Gear 24" wheeled bag (from Costco) that had room for most of her stuff with a large handbag for extras.
This choice worked well, because I could carry my bag on top of my wife's roller bag if I got tired, and she got a break from carrying her heavy luggage. With the heightened security, all bags needed to be checked at the airport anyway, and even with stairs and rough streets, a tough single bag can be dragged pretty much anywhere. Just don't get a bag with a single bar for the extension handle or whatever you put on the bag when walking will constantly fall off.
We also needed a computer back-pack for out laptop and digital camera. A couple of good ones are the computer daypack from JanSport and the MacroLoader pack from eBags.
I made a mistake in not bringing a small day bag. I have a small MountainSmith bag that I love and is perfect for a guide book, cell phone, flashlight and a camera, but I left it at home in the interest of packing light. I could have used this bag almost every day. The only good thing is that I kept busy the entire trip when my wife was shopping, looking for a good European-looking shoulder bag. I finally found one in one of our last days in Paris that was perfect, but the trip was almost over. It made an excellent travel gift for my son when we got back however.