#1 there is no perfect bike.
#2 one bike to do all these things is going to be a compromise on all.

Instead of telling you what bike to buy might I suggest you visit a number of Local Bicycle Shops (LBS) in your town, city, village, etc. Choose the one that treats you the best and then listen to their advice and ride a variety of styles that would work for what you are looking to do. Let them know your price range up front but understand that entry level bikes come with components that will have a finite lifespan. If you end up riding lots or hard or neglect maintenance the life might be shorter. Choose the one that appeals to you not just by ride feel but also the looks. It is more likely you'll ride a bike you like.