For temporary water filtration options, faucet mount, pitcher, and countertop filter from Pur, Brita, GE, or similar brands are excellent for a home or an apartment. I have used all of them but maintenance or the frequency of filter replacement can be the ultimate decisive factor in choosing them over other types.  

Pitcher and faucet mount filters are the best and quickest way to get yourself settled in a new home or apartment until you can find out exactly what makes your water taste or smell bad.  From that point, you can make the best decision whether you need a whole house, countertop, reverse osmosis filter, or any other good sink filter system. Or perhaps the water may be hard and a softener will be the option.  

Pur and Brita filters are household names. Chances are a neighbor will suggest them if you just moved to a new house or an apartment, especially if you are not yet familiar with the quality of drinking water in your new environment. The limitation of a faucet mount or pitcher filter is the frequency of replacing their cartridges every 2 to 3 months. It could be less than 2 months if the water is really dirty which could make these systems very expensive on the long run.