Hi,
This is an old thread, but I thought it would be worth pointing out that the answer is probably different today than it was in 2012. Today, direct digital conversion is probably the best idea for a DIY project like this, since you're only interested in frequencies up to 50 MHz. 100 M sample/s is enough to digitize everything from 0 Hz to 50 MHz all in one go, and that kind of ADC chip costs less than $20 in single unit quantities (as of 2023). You would still need to design input conditioning (attenuator, low pass filter, amplifier) to get the input signal's amplitude into a range suitable for the ADC chip, and a microcontroller with enough speed to capture a run of samples into ram chip, and then shuffle them from there into a PC over a USB connection, but after that the spectrum analyzer becomes a software problem. Research free open source "SDR" (software defined radio) projects to get ideas from things other people have done.