If I read your post correctly, I thought you mentioned wanting to train for triathlons. In doing so, I would think the distance you're looking to ride (the same distance I commute) would be beneficial to your training regimen. I could be wrong since I don't know exactly how triathletes train for the cycling portion. Still, the distance is more than doable especially when you're about half my age.

The weather issue is moot. I personally try to avoid heavy rain or thunderstorms if it means doing so in the dark. If I do wind up commuting in those conditions, I'm just more cautious than usual. It's not the weather but the drivers that make it an issue for me. Other than that, I'll ride rain or shine.

Just be ready to spend some money on gear if you don't already have it. If you have $800 for a new bike and that's it, I would look for something in the $500-600 range so that you have some money left for proper gear. This time of the year, I'm heading out at 5 am with ear muffs, tights and toe covers. Decent set of cycling tights alone might set you back $70-100. Not to mention all the other garbage you'll probably want or need (lights, helmet, rack, etc.).

Good luck!