What do you want? Price, speed, puncture protection, smooth ride, durability, forgiving, weight?
Bigger tires can be a lot faster than small tires - the one exception being weight. for example, I have a 60mm tire that has less rollling resistance than any of my 23-28mm race tires. Go figure. The down side is weight - heavier tires are just slow to accelerate. Still, at 15mph, they are hard to beat speed/effort wise.
So, if you are not concerned about weight, get the biggest tire you can fit on your frame. 35mm is a nice side (and yes, it is easier to put large tires on a bike with disk brakes, since you don't have to worry about caliper clearance).
Tread does slow a tire down a lot on the road, so I like slicks or semi-slicks for commuting
I have gone down fast and hard with ZERO warning on black ice. Really, stay home or get studded tires. Something simple like a sprained ankle (or worse) just isn't worth it.
I like having a second set of wheels. Nashbar has some well priced stuff. Then again, I also like tubeless at 35mm or wider.
I've seen people get really nice race tires and then whine that they are not good tires for touring.
Personally I don't like your tires since they are so darn heavy, and are small for a 28mm. They are heavy, slow, and have a lot of rolling resistance. I threw mine away.
Higher thread count is not more puncture prone in my experience. There are too many other factors to consider.
Personally I like supple, smooth riding, light fast tires. You may want something different (especially for touring)