and without running any numbers....

Off hand, I think you could pick an Apollo body or similar NEO as the desired target. You'd want one whose orbit is as close to Earth's as possible.

The duration of the mission would depend on the desired target and the total delta-v capability of the vehicle. If the delta-v capability is minimal, then the mission would probably last about one year. You'd boost into a heliocentric orbit with one apex at the Earth and the other at the target. If you have greater delta-v capability then you wouldn't have to fly a Hoffman minimum energy transfer can you could shorten the mission considerably. Without having a definite target, it's almost impossible to determine which propulsion technology would make the most sense.

If the total delta-v requirements aren't too high, then you could probably go with hypergolic propellants like used on Apollo and Soyuz. If the requirements are marginally higher then perhaps ion propulsion would be a good bet. I'd love to use something more energetic like VASIR but that's quite a few years in the future.

Your basic issues involve things like life support without resupply, crew health and fitness in a cramped environment, system redundancy, etc. The current Soyuz capsule is kind of cramped for a long duration mission because there isn't room for a lot of supplies or to exercise. The Soyuz also lacks sufficient radiation shielding for flights beyond the van Allen belts and the heat shield is only designed for a return from LEO. I really don't think it would be easy to modify the Soyuz for the mission. Ironically, one version of the Soyuz capsule was designed for their moon project and it would be a lot more suitable than the current one except for the cramped size.

I really have to go now but I'll try to find some more specific info. Interesting question. Personally, I'd like to design a vehicle specifically for long duration manned interplanetary spaceflight that could be suitable for this and other missions.