Quite an item - very attractive except for the price! My experience has been that riding on streets, sharing the puddles with car traffic, is that water splashed by vehicles is the biggest source of moisture, so an umbrella is almost irrelevant. For me, the biggest rain issue was keeping my glasses clear enough to allow safe navigtion. What worked fairly well was a brim on the helmet or cap. Even then, I might stop every ten miles or so to clean my glasses.

I have found that 37/38mm tires are quite versatile, working well on both pavement and on hard packed soil/gravel. It all depends on the surface of your bike path.

The ultimate frame for commuting is some sort or another of touring frame (mine is a Surly Long Haul Trucker) - stable and serene. But frankly, any frame will get the job done. Getting the right tires is super important.