Well to answer your first question...
Wireless N is newer and greater than Wireless G by all standards. It uses more bands so there is less signal lost and a longer distance range. It also costs a lot more. The limit of your ISP and network will tell you if it's worth the cost or not.
Wireless G max transfer is up to 54MBps and 100 feet distance across the network.
Wireless N transfer 54 Mbit/s to 600 Mbit/s and 700 feet distance across the network.
So if you have a large network or over a large distance, shared internet, stream music, games and video or data across it wirelessly, etc, go for Wireless N. Great if all your files are on another shared computer and you just want to stream to the other computers. It is compatiable with Wireless G devices, but they will limit it on their end so it's best to update the lot, router and each wireless device connecting.
Wireless N does not however speed up your internet connection. The connection itself will limit the speed, since not many people have 54MBps+ internet speeds, the cost of the upgrade isn't worth it if not networking. The ISP your with deals with that end and packet settings, etc.
Having a Wireless N network card connecting to a Wireless G router is a waste too (weak signal in). It should at least be the other way around. The router should be Wireless N, then update the network cards later or at the same time.
To me it sounds like your having low signal and signal lost. Moving the router away from walls, up high, and away from electric devices which might interfer might help a lot.