Whatever you do to cover and install, it will raise your floor that much higher. Transitions into other rooms will not be the same, and doors may have to be cut. Also, the toe-kick will be that much 'shallower' under your cabinets and it's possible that your feet won't fit under there (maybe if you're just wearing your workboots.) These are just some thoughts to consider.
If you can manually rip up the old flooring while it's still attached to the underlayment (no saws, no power tools, no sanders) where you don't create any 'dust', you can remove it yourself. The only remaining trouble is: Disposal. For this, you can check around local building sites where there's a Foreman and ask if you pay, say $50, can you bring your 'hazardous waste' and dump it in his hazardous waste dumpster. (You may need to look for a home or business that's being renovated. Usually, new homes don't have 'hazardous waste', per se ...) Make sure he's THERE when you bring it because next thing you know, someone reports you for Illegal Dumping! Of course, get his name and company.