Hey demetal,
While the project sounds like a good idea, it might need to be scoped with a little more detail - it's like saying you want to build a racing car around a spark plug!
The 16F877A is a nifty controller, but even at this stage I'd be skeptical of its utility in a VNA design, primarily due to it's limited (RAM) memory. Since you'd probably want to store many sample points, configuration data etc, I'd opt for a micro with a greater dataspace... and in all honesty I'd probably reach for a DSP with an external memory interface. (Not to mention the '877's best "PC interface" is probably its UART. The PIC18F4550 features as many IO's and a USB interface to boot...)
The micro is an incidental part of the design though - the heart of a network analyser is in its reflection bridges, synthesisers, gain and phase measurement engines etc. I presume you're planning an RF design? (There are a few audio/LF designs on the 'net) What frequency range? Thanks to the wireless revolution, there's a bunch of RF IC's available that would make a low cost DC-2.5GHz design quite plausible.
Good luck!