Receive several fm-radio stations at the same time (~10-20 MHz wide summary at 90MHz radiofrequency)
The second technique you mention is the way to do it, using what is called a "Software Defined Radio" or SDR. Many radio amateurs are using SDRs, and the simple ones are very cheap, about 30 dollars for a kit that down-converts the input into in-phase and quadrature baseband audio output which is fed into the stereo inputs of a PC sound card for digital signal processing. However, they are using relatively low-frequency signals on the HF amateur radio bands, and the hardware doesn't use any exotic components. Digitising VHF signals as you require and receiving several channels simultaneously is going to be rather expensive, the ADC alone is going to cost about 50 dollars and you will also need an FPGA and a DSP, unless you convert down to baseband and do the DSP on a PC. You will need a lot of high-frequency design experience, be able to develop code for the FPGA, write DSP code and be able to design a high-speed multilayer PCB, so you should start studying. :)

As for cost, I'd estimate 500 dollars for the hardware, including the PCB, assuming you designed it yourself.

Linear Technology makes suitable ADCs that can downsample at 750 MHz! They were good enough to give me a couple as free samples. I have suitable FPGA and DSP boards, so it's just a question of putting them together. :)