Newer Dolphin versions are more likely to have fixes for Netplay. While most compressed game formats are compatible with standard ISOs (with NKit being a notable exception), it is heavily recommended that all players use identical dumps.
Because the latency (ping) of the internet connection determines how low input latency can get, using Ethernet instead of Wi-Fi usually improves the gameplay experience.
However, the internet demands rapidly increase as more players are added. Bandwidth requirements are very light: any DSL or Cable internet connection should do.