I suppose you meant Interplanetary space ship and not planetary.
The design will be highly dependant on the kind of propulsion use for this first spaceship.
If we still use chemical propulsion, ya it could be similar to the Apollo. And this will probably be the case. Check the Orion MPCV. It still could be cancel, but it seem that this would be the spacecraft use for the next Moon landing and eventually Mars landing. It use pretty much the same concept as Apollo.
Still, maybe in the future even if the Orion MPCV is working fine to reach the Moon, the NSA and ESA will prefer to develop the new vehicle to reach Mars, using new propulsion technology.
Ion thrusters, Electrothermal or Electromagnetic propulsion usually have low trust, but high specific impulse making this kind of technology really good for long travel time. These technology would use more electric power than anything we had ever launch in space. Maybe this spacecraft could be powered by a nuclear power plant. This would greatly change the visual aspect of a spacecraft since the reactor will need to be as far as possible from the crew space. But personnally, i highly doudt that a nuclear powered spacecraft would be launch in the near future. The obvious political, social and environmental problems caused by the launch a nuclear reactor on the top of huge rocket. Even if the technical problem are not that difficult, especially with not dynamic power conversion technology that begin to emerge, this kind of technology in space is a long way down the road simply because a lot of people will try to stop it.
If i personnally believe that electric propulsion will be one of the core of any future golden age of interplanetary travels. This kind of technology probably won't be ready to use in the first travel to mars.