A properly engineered, high quality portable set can produce "cleaner" power than what you get from most power companies. Conversely, a thrown together set, made with the cheapest parts available will often produce something barely resembling a sine wave.

I know it seems tempting, but don't do it. There's no way you can reconcile this approach with code. For one thing, you can't legally stick a plug on the the end of the permanent circuit wiring which is most likely either metallic sheathed (AC or MC) or NM-B. For another, the furnace installation specs almost certainly call for hard-wiring on a dedicated circuit.

Wayne's solution is by far the best way to go, IMO. Aside from the fact that you'll probably need to replace the circuit wire with longer length(s) (since the switch and inlet will mostly likely be located on the outside of the house), wiring the x-fer switch is not much more difficult than installing a junction box and receptacle.

As far as the "dirty power" concern, there's another factor to consider, in addition to generator quality. As often as not, so-called "dirty-power" problems happen when a generator is pushed to (or even a bit beyond) its rated running capacity. This often occurs briefly when motors start up. Because both the voltage and frequency (hertz) are tied to motor RPM in most generators (generators with inverters excepted), when the generator engine speed bogs down, power quality suffers.

Anyway, to avoid dirty power problems, don't skimp too much on generator capacity.

One final note: Before finalizing plans for reworking the circuit to include a transfer switch, make sure to factor in how the thermostat(s) get power. Every once in a while, you hear of someone installing a transfer switch without realizing that the transformer for the low-voltage thermostat gets it power upstream of the transfer switch. It's not all that likely you'd encounter this problem, but it is possible and, thus, should be part of your "checklist".