TWO Gateways required to save costs...
What's really needed are TWO "Gateways" - one in Earth orbit and the second in Lunar orbit.
Smaller rockets (taking up maybe Crew Dragon or even Soyuz capsules) can then be used to transport the humans up to the Earth Gateway, where they can then switch to another rocket which just travels from Earth to Moon (and hence Lunar Gateway) and back again.
Experiment equipment, and cargo (inc food, water, oxygen etc) can be sent to Lunar Gateway in advance of crew arrivals.
And a version of Crew Dragon, with some added rocket power, could be used as the Lunar Lander, as with 1/6th the gravity, a small re-useable craft that just needs to carry humans could be used easily enough.