Basically, you CAN keg anything... do you want to, might be a different story. I've never kegged anything but beer, so take this fwiw.
Hardware: If you want to make a chest freezer into a large kegerator for relatively cheap, you can get the chest freezer and then convert it into a "keezer" via instructions you find online; it is pretty simple and will house four or five, 5gal kegs/taps.
A regular size commercial kegerator designed for one standard half barrel keg will hold three five gallon kegs and up to three taps.
I bought (and still have) literally the cheapest kegerator I could find. In terms of temp control, it's fine. The taps and tower hardware that came with it were pure crap, so in the end I spent several hundred more to upgrade this to good stuff and it came out to about what I would have just spent on a better kegerator in the first place. I've used Perlick and Intertap faucets. I much prefer the Intertap. Faucets and beverage line are not a place to cheap out. Both are critical to having a positive experience.
Thoughts on champagne: if you are talking about buying a keg of it already made, I would want it to be precarbed so you aren't having to spend your own time and CO2 getting it carbonated. A quick google says the carb level in champagne is around 5-6 volumes, which is obviously a lot. You are going to need a lot of line and probably a flow control faucet to have any chance of getting this into your glass without it being a foam bomb.
Whiskey (or anything else that isn't supposed to be carbonated) I'd keep in the bottle and not in the keg... the reason being that if it is under any kind of serving pressure, it is going to absorb Co2 and become carbonated to some level. You could be extremely diligent about purging the pressure when you were done pouring on it for the day/night, but even then, over time I think you're likely to get some carb level in it.