This is what most people think of when you ask about road bikes (or 10-speeds, ok, it says 12 speed.
)
I didn't do an exhaustive search, but this would make a good road bike for your needs. Albeit, on the top end of your budget.
Nishiki Olympic 21” Road Bike 12-Speed $300.00
That is, if you are actually looking for a road bike.
Are you doing year-around riding?
Perhaps get a road bike for those spring/summer/fall days, and hunt for a beater MTB for the mid-winter riding.