Welcome! Sure, a Trek FX will do those jobs well. Others in this market include the Cannondale Quick, Fuji Absolute, Giant Escape, Jamis Coda, Raleigh Cadent, and Specialized Sirrus. There are others, I'm sure; these are just the more popular ones from major brands. These will all fit your body just a little differently, so test ride as many as you can before you buy. You may consider disc brakes -- they'll be advantageous in wet weather.