240x160? My mother's Atari 7800 has a higher resolution output! Thank goodness the GBP upscales it to 480p.
I remember using tunneling services, GameSpy had their own XBox Tunnel service for a long time. That is how I first played Halo CE online. Warp Pipe was the first one for the GameCube, eventually i started using Xbox Connect for the Xbox and dabbled with Xlink Kai with my friends who had Macs and wanted to play Halo (since XLink was the only xbox tunnel software that ran on a mac)
I've used Warp Pipe some 10+ years ago. If you don't feel like spending that much money on BBA get a Wii, tueidj (https://sites.google.com/site/wiiflowiki4/devolution-setup) has emulated the modem adapter that works through the Wii WiFi so you can play LAN games, and online too if you want to try Phantasy Star Online
Similar in processing power (actually the GBA had a more powerful CPU), but Nintendo cheaped out with the screens to keep the costs low.