There are good options in your price range for what you want to do.

I strongly advise against a "department store bike," also known as a "bike shaped object" (BSO). You need a bike that was assembled by someone with knowhow, and you will not find that at Walmart or Target. Probably not even at your local sporting goods store. Go visit a local bike shop and let them know what you're looking for. There are definitely decent bikes that can be had in your budget.

I started commuting on a 10 year old hardtail mountain bike that was 350 when it was new. It was a reputable brand and has been handed down to a friend who still uses it.

You may want to leave room in your budget for helmet and accessories depending on what you want to do and when you ride your bike (at night, or in the winter, for example.)