unfortunately, the ship would have to be extremely large to accomidate enough plants for one human so the idea of an indefinite escape pod is out of the question.
Exactly how large, again?
The exact numbers depend a bit on how far you want to go from a light source. Here's the basic assumptions:
1) I'm going with the solar panel design, because it scales better at long distances form the sun then the direct plant design does, and captures all types of light a bit better. I'll be using a solar panel efficiency of 80% (which is about double our current best ones, but still well under the theoretical maximums of ~90-95%).
2) We're going to go out to pluto and back.
3) You're going to grow sugar cane, since it has the best caloric storage of about pretty much any edible plant. I hope you like sweet things.
With these assumptions each person is going to need to have about 150 m^2 of solar panels stretching out on the outside of your ship, and probably around a 10m x 15m x 20m square cube to actually grow their sugarcane in, based on the normal adult human energy consumption.
To put that in perspective, each human is going to need about a volleyball court's worth of solar panels, and 1.2 olympic sized swimming pools worth of space to grow their food/purify water/make air (though you might need additional space for more air/water purification, I haven't run the numbers on those aspects). That's on top of whatever space you actually need for the ship itself and any area for the person to live in.
Alternatively for interstellar distances you may want to go the hydrogen scoop method where each person would need about 437 m^2 (2.7 volleyball courts) worth of scoop on the front of your ship to harvest the hydrogen needed when traveling at solar escape velocity speeds; the main benefits being that while the amount of solar panels you need keeps increasing as you go farther from a star, the amount of hydrogen scoop area you need remains relatively constant no matter where you go in the milky way galaxy.