I agree completely with Ballan's suggestions. Moving from an 802.11g to an 802.11n wireless router will give you greater range and eliminate the interferece from devices like cordless phones and microwave ovens, which use the same frequency band as 802.11g. That means, though, that both ends of the wireless connection have to be 802.11n. Your computer will need an 802.11n wireless card or external adapter to take advantage of the 802.11n access point.
One thing you can try with your current 802.11g setup is to switch the wireless channel. There are 11 channels available for the communication between your computer and your wireless access point and you might be able to get rid of the interference from other devices by switching from the default channel to one of the other ten channels. It won't help if the problem is signal strength but it might help if the problem is interference.
With the Apple Airport Express you specify the channel in the setup utility that is part of the system software. With other wireless routers you'll have to do it through their setup application or through browser access to the setup parameters. They're all different so you'll have to wade through the setup instructions that came with your router.
