For a complete beginner, what bike would you recommend? I live in a tiny apartment on the 4th floor, narrow stairs and no elevator.  I'm looking to buy a bike, and planning to put in 50-60 miles a week at least.  Could you recommend a bike in the 300-350$ range?  It would be better if it is a foldable bike
I'd recommend getting a cheap used aluminum frame bike (a beater), a good lock, and a bottle of oil.  Then, I recommend you lock it on the street most of the time.  I recommend cheap so that you won't worry about it while it's parked on the street.  I recommend aluminum so that it is light enough to haul up to your apartment for those extended periods when you won't be riding it (also so it doesn't rust).  

It might take a beating getting stored outside, but if you ride it frequently that'll battle the effects of the weather (as will the bottle of oil).  One of my schools (in the midwest) had nearly 100% outside storage for student bicycles.  It snowed, rained, etc.  But, as long as the bikes were used and maintained regularly, they ran fine.  (The ones that sat for a long time eventually turned into piles of rust.) If you spend, say $150 or so, you'll have enough left over for periodic tune-ups on your cheapo from your local mechanic.  

Also, if you store it outside, you'll be more likely to ride it for quick trips than if you have to haul it up and down 4 flights of stairs.