Nobody is going to Alpha Centauri in anything less than a nuclear (fission) -powered spacecraft, which makes it rocketry crime that Nixon cancelled the Nerva Program some 50 years ago.
Humanity is likely to colonize the Oort cloud eventually, making for a seamless colonization wave into the next star systems over. If we learn to live inside hollowed out resource rich cloud bodies, we would split into an astronomical number of species and few will see any reason for a costly and forgotten gravitational well transit to reach more resources.
But lets imagine that you want to try a non-generational ship. NERVA was not developed for anything else than to cut interplanetary transit time in half. What early rocket scientists wanted to do was what Germany did when they couldn't stabilize early jet engines, simplify to a pulse engine. In Germany it was the Vi1 engine, in US it was the Orion engine - nuclear bomb pulsed fission/fusion. Such an engine can drive a ship at about 5 % of light speed, which NERVA cannot. If we had wanted, we could have (poisoned Earth and) sent a probe to the stars in the 50s.
Launching an Orion from a Mars colony would be a great attempt along those lines, the planet is already radiation poisoned due to the thin atmosphere.
This also eliminates all of the wind resistance which also burns a lot of fuel. They might even be able to make the entire trip with just one engine, which would really save on fuel, while also saving wear and tear on the other engines.
The system is designed to use as much thrust it can manage to cut down on travel time, in fact they have said they want to add three more engines on the upper stage.
What "wind resistance" are you talking about? A launch system to low Earth orbit [LEO] suffer what is called "gravity loss", which is the net performance loss due to cancel the force of gravity - still 60 % of surface gravity at LEO - as they want to attain orbital velocity. The aerodynamic losses mainly consist of having to compact the atmosphere at supersonic travel around max Q as it leaves the troposphere at around 10 km height - the Karman line for a stable orbit is ten times higher at 100 km. I can read that the total losses for
atmospheric drag and
gravity drag are 1-2 km/s out of the additional 8 km/s at low Earth orbit so in total a delta-v demand of 10 km/s for launchers.
It is the high orbital velocity of Earth's huge gravity well that is the problem. After refueling you see that the remaining delta-v work to be done is much the same. "Earth’s surface to LEO is also nearly equal to that required from LEO to surface of Mars."
At this present time, the only way to safely go to Mars is with a heavily shielded rotating structure. Lots of mass. And lots of supplies.
The Starship strategy is - has Musk recently noted - to have the 9 m diameter ship rotate. The rotation acceleration that you can take without adaptation are equivalent of Moon surface gravity and there are hypotheses that long term adaptation would allow a rotation speed that gives an acceleration equivalent to Mars surface gravity.
The project will launch construction mass (construction material, construction equipment, metalox production plants for propellant and air production) and supply mass with automated ships before they send the first manned crafts.
The manned crafts will likely not be heavily shielded since they transit for a few months, it is not two year long NASA return missions but colonization transits. Instead they will have their water supply act as a radiation shield specifically for solar CMEs, which will damage humans.