Well mtofu:
1) Present day CPU's are more than capable of processing more data then what can be shoved out of a gigabit network port, so basically every present day PC should be capable of this.
2) RAM will only be an issue if Vista forces your OS programs to use the page file for running applications, since any streaming data will have a data read bottleneck at the HDD read speed. So if you have Vista 2GB will be enough, if you get XP you could probably get away with 512MB. Although present low end Vista PC's (even from Dell) will have enough RAM to do your desired application
3) Video converting programs, depending on the program will be entirely dependent on the CPU/RAM. Now if the program is only capable utilizing a single core (not multithreaded), last gen processors would probably be just as good. So a current multi-threaded converter will get faster with upgrades to the CPU. The RAM will probably be a null here too, just as long as there is enough available to run the program (basically looking at the recommended RAM usage requirements of the program), anything extra will just be wasted space anyway. So I highly doubt any PC will have this limit, even a 2GB Vista box (it would be worth checking up on the program though).
4) The only number crunching your PC is going to do is by the network device (i.e. converting data into IP packets). Relating back to point 1, the current gen CPUs and RAM are all capable of doing stuff way beyond 10/100/1000 networks.
If you have some more questions I might be able to help, but my answers are based on the assumption that playing media files on the PS3 is basically having either the PS3 load the file to its local HDD or reading the file over the network from your PC (similar to PC to server access in a business network).
EDIT: On a side note, in my line of work, I have found serious issues with actually having 10/100/1000 consumer grade switches/routers capable of transmitting more than ~250Mb/s.
