Connecting a different router shouldn't cause a problem if you do need to revert to your existing router.
When making any changes to the "wireless" settings in a router, it should always be done while connected by ethernet cable, not wirelessly. The reason for this is that, as soon as the changes are saved, the current settings become invalid and a wireless connection will crash.
The changes you may want to change in the wireless settings are the SSID (network name), Channel Number (in case of interference from other wireless devices) and the Security (WEP/WPA/WPA2). The default settings for these should be OK for you to get started though.