2-channel will work, using passive crossovers supplied with the component set. 4-channel will also work, as these days most decent component sets can be bi-amped - meaning one amp channel per speaker.
Bi-amping still utilizes the circuitry inside the passive crossovers (coils, resistors and caps) to perform the crossover functions of filtering out the signals that are not optimal for their respective speakers. I.e., tweeters get a HPF (high pass filter) made from capacitors which will "filter" out or attenuate lower frequencies at a rate that doubles for each octave below the cutoff point. So... if you have a HPF at 6dB/oct at 5kHz, then at 2.5kHz a signal of the same amplitude will be attenuated 6dB. Likewise at 1.25kHz, it will be cut down by 12dB. At 625Hz, it will be reduced by 18dB. The same principle applies to the LPF (low pass filter) applied via coils wired in series with the midrange or woofer.
Keep in mind, the decibel scale is logarithmic in nature. 1dB is theoretically what we can discern as a change in volume, while 3dB is a "perceived" doubling of volume.
My personal preference would be a 4-channel for bi-amping, unless you have a very high-quality passive crossover and speakers that really shine with a great amount of power AND you have access to a very high-powered 2-channel amplifier you would like to use. Here is why:
Some passive crossover networks have a built-in configurability (is that a word? lol) to allow you attenuate the tweeter level. This is most notably necessary with metal-dome tweeters, which some of us will remember in the MB Quart components, etc. Some people love that high end brightness or "sizzle", personally, I find it a bit fatiguing very quickly and prefer soft-dome tweeters made out of cloth. Though I have now moved to HLCDs and never want to go back, lol. Beside the point. On the old MB Quart crossovers, they had a jumper you could set to different points to have the tweeter at 0dB, -3dB and -6dB. This was accomplished with resistors in the circuitry that would tone down the output of the tweeter, so people like me could save on headache medicine.
That will work to a degree, but personally, I prefer a 4-channel amp for components, because it offers you the best ability to individually tune each speaker for level. Keep in mind the path-length differences and such. Phase can be adjusted for each speaker with wiring. But level... well, level is more easily adjusted if you have a 4-channel amp. Many of you might think this is simply overkill, and for your application, perhaps that is true.
But I find it to be the best balance between bang-for-buck, configurability (there's that made-up word again - perhaps "flexibility" is better), upgrade-ready and ease of use/installation.
Just my $0.02.
Ok.... more like $0.03-0.04? lol
Hope that helps a little bit.