It mostly depends on the clearance under the brakes. With 49 mm drop brakes (the common road bike size) you are lucky with 28 mm tyres, but often 25 mm is the maximum. With 57 mm brakes 32 mm tyres are often possible, sometimes even with mudguards. Go for the widest tyre you can fit, and on a bike like this don't take more than the minimum of luggage. My favourite in fast touring tyres is the Panaracer Pasela. On a bike like this I might even go for the non Tourguard version (no puncture protection) because it is faster and more comfortable. As a comprimsie you could fit a Pasela TG at the rear (where it is most needed given the greater weight) and a non TG at the front for more comfort for your hands. Pasela's are tue to size, unlike many other tyres that are narrower in reality than their spec. So measure your current tyre to know its real size.
Willem