For MOSFETs the threshold voltage is nothing to do with switching it on,
its the point it switches off. Unless you are planning to use a non-zero
voltage to switch it off its irrelevant.
You look for something like "Rds(on) = 0.04 ohms for Vgs=4.5V", meaning it
needs 4.5V of drive to switch on to that resistance. The lowest Vgs quoted is
the minimum gate drive voltage.
A CMOS inverter takes no current when the inputs are static (well, a few nA only),
any pull-up resistor will take orders of magnitude more current, unless in the 10M
ohm range, when noise pickup will be a show-stopper.