LAMP/Nagios/MRTG/Ossec
 

Best network monitoring box you can build for zip $

If you can define what "best" is, we can answer.

Otherwise, "best" is whatever tool(s) you find that fit your NEEDS. Nagios is pretty much the 'standard', but there is also zabbix, MRTG, and a host of other tools you can use. You don't say what "network monitoring" you want (IO on individual network ports? Server uptime? Disk usage? process(es)?), so it's hard to say. There are MANY absolutely free Linux monitoring tools, some of which overlap, some work together well, some COULD work together well, and some may do exactly what you're after without ANY modification.

Again, define what you're looking for, what hardware you're going to run it on, and version/distro of Linux, and we can try to help.