Upgrading Verizon FiOS issued wireless G router

So I have a Verizon FiOS issued wireless G router (UltraLine Series 3 Model 9100EM). The range on this router is terrible when I'm anything more than 10 ft. away from the router. What new wireless router do you guys suggest? I will probably go the wireless N route, but unsure if I need dual band or not. I mainly use my wireless in the house anywhere from 20-45 ft away from the physical router. I stream quite a bit of stuff on my laptop and computer so getting a strong signal with good speeds is deal.

ps - my internet is 35/35 speeds and I wasn't getting more than 1-5mbps DL speeds when I ran speedtests. The house I'm in is an older home built in the '60's but I don't know of any interference issues other than cordless phone and microwave that would get in the way.

Thanks for any suggestions guys.