If you are having difficulty with connection dropping or connection speed, first look for a higher gain antenna to put on the router and PC. Higher gain antennas send and receive stronger signals than low gain antennas.
This is a 9db gain antenna, and at only $10 will give your router a real kick. Most OEM antennas are 0-3 db gain.
A PCI slot card like this will let you get the antenna up where it will send and receive stronger signals because there will be less in its way than the built in antennas in desk top PC's.
Most any router and wireless card should have enough power to operate in the average size apartment. But sometimes apartments have obstacles, like lots of pipes in walls, load bearing solid concrete walls, etc blocking signals that a regular house does not have. Placing the router at eye level or higher on a book shelf usually helps improve signal quality.
For example, my Linksys wireless G router on the second floor of my house can be picked up by my neighbor about 800 feet away. Put the same router in your apartment, and you may not be able to pick it up down the hall 100 feet away.
And don't forget to encrypt the router. At a minimum, it will keep your neighbors from sucking up your bandwidth for free.
If none of that helps, get a wireless-N router rather than a wireless-G router. It operates on a higher frequency that passes through obstacles that block wireless-g signals.