You can by cheapo vinyl planks for $1 a sq/ft - install can be yourself or prices vary greatly. You can get cheapo carpet for about the same plus $100 for install. Will you be happy with cheapo tiles (I am talking super cheap)? Will your landlord be happy with the cheapo carpet (probably not)?
Also if the carpet and padding are in good shape you could roll them up and store them if that is an option for you. Would need landlord's OK and you would have to pay to have it reinstalled.
If I was in the same dilemma and planned on staying there a while I would go talk it out with the landlord. If you put something decent in there a majority of landlords would let you do it - given the job was finished right and you didn't mess up other things. There are some landlords that would even pitch in to pay for all or partial the amount for the flooring. This depends on the landlord, current carpet condition, how long you will stay there... There are also some landlords that don't trust anyone and won't let you touch anything. You need to got talk to your landlord and then ask a flooring question after you have more or know your options.