You don't need a router to connect to servers. All you need is an internet connection, even a dial-up would do it.
If you want to host a server, you must have a fast internet connection.
I would recommend you using port 28000.
Ping is a computer network administration utility used to test whether a particular host is reachable across an Internet Protocol (IP) network and to measure the round-trip time for packets sent from the local host to a destination computer, including the local host's own interfaces.
Ping operates by sending Internet Control Message Protocol (ICMP) echo request packets to the target host and waits for an ICMP response (or a pong). In the process it measures the round-trip time[1] and records any packet loss. The results of the test are printed in form of a statistical summary of the response packets received, including the minimum, maximum, and the mean round-trip times, and sometimes the standard deviation of the mean.
The use of the ping utility is usually described as pinging a host computer. Ping has various options depending on the implementation that enable special operational modes, such as to specify the packet size used as the probe, automatic repeated operation for sending a specified count of probes, time stamping options, or to perform a ping flood. Flood pinging may be abused as a simple form of denial-of-service attack, in which the attacker overwhelms the victim with ICMP echo request packets.
