Unless you're racing in the rain the Zaffiro is plenty good enough. I had a set of those some years back and they were actually fine in the rain, they just didn't last as many miles as the Rubino did. The problem is when the tire gets wet is that it picks up stuff off the road, and some of that stuff will flat your tire, this is true with any tire, but the Zaffiro isn't as good against flats vs some other tires, so you might want to get a pair of Rhinodillos flat liners.
But if you want to spend the least amount of money possible the Zaffiro Pro G 2.0 is probably the best tire for the money. Also for that 15 cost range I wouldn't worry if they're folding or not.
Another tire to consider is the Conti Ultra Sport III, about the same price as the Vitts but the Vitts is a better tire.
Of course, the flat liners will add to the cost of the tire budget, but those are transferrable, so when the Vitts wear out you can transfer the liner to your next set of tires, so they're just a one-time expense. Tire liners work a lot better than flat-resistant tubes, also known as thorn tubes, plus they're lighter in weight even when you add the weight of a regular tube.
By the way, if you have to ride in the rain, keep your tires off of painted lines and metal grates, and take extra precautions, especially for the first hour of rain as that rain will lift oils off the pavement and make the road slick for bicycles.