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Hopefully this isn't a duplicate; I wasn't able to find another question which addressed this, at any rate.

Let's say I have a generational spaceship going off to another solar system to establish a colony. The problem is, I need to feed my colonists for generations, not to mention for a while once they land on their new planet while they begin terraforming it. Fortunately, I have artificial gravity and power generation on the ship taken care of, but there's no way I can do livestock or dirt-grown gardens.

I know a few basics: I will probably be growing my plants hydroponically with nutrient recycling from waste, and bamboo is likely to feature heavily, as it can also be used as a construction material. Cloned meat is a possibility as well. But my problem is, I'm not exactly a food scientist, and have no idea which plants would take well to hydroponic cultivation in a cramped spaceship. what are my colonist's main foodstuffs likely to be? Potatoes? Mushrooms? Are apples a realistic option? Is anyone going to bother with wheat, or would that take too much processing to be worth it?

My question, basically, is which plants would be the easiest to grow hydroponically in deep space, and which would be inviable. Some basic GMOs are a possibility, but I'd really prefer not to just handwave 'everything can be cloned, pick any foods you want'; I'm only barely conceding cloned meat because it's starting to become practical now.

The best answer will account for nutrition and ease of cultivation and will include specific ideal staple foods or categories of staple foods (e.g., "Your colonists will eat bamboo and root vegetables for fiber and carbs, mushrooms for protein, and leafy greens (like kale) and chili peppers for vitamin c. Your colonists will not have many fruits which grow on trees or grains like wheat, corn, etc.")

Protein:

Crickets are not only the food fad of the moment but they are easy to raise, don't have the same ethical problems to kill as most meat animals, and are loaded with protein. My spouse thinks they taste terrific. They can be even roasted or ground into a flour for cooking.

Oysters can be raised in underwater farms using waste (manure). This can also be done in a recirculating aquaculture system. In addition to high protein, they've got a ton of nutrients.

Legume seeds also have a fair bit of protein and aren't hard to raise. The bonus is that legumes fix nitrogen in the soil (meaning you grow them with other crops or you alternative seasons). Given that your ship is generational, you might use some soil for your gardens instead of just hydroponic systems. Think edamame/soy, chickpeas, lentils.

Carbs/Calories:

Potatoes are pretty easy to grow in a lot of situations. Heck, even on Mars.
Sweet potatoes are similarly easy.

Jerusalem Artichokes aka sunchokes are tubers from a plant related to sunflowers. They can be grown hydroponically.

Rice is already being grown hydroponically.

Fats:

Seeds from small plants are the way to go. Some smaller varieties of sunflower, hemp, flax, canola, etc. Many of these are already grown hydroponically.

Vegetables:

Leafy Greens such as lettuce, spinach, chard, kale, basil, mint, other herbs, are also easy to grow hydroponically.

Cucumber, Tomato, and other vine crops, also easy.

Fruit:

Trees such as apple are harder but not impossible. Apples can be shaped easily so can turn into fences (with wire to help hold it) or other flat surfaces, or can be grown normally as part of a park for residents.

Don't forget fruits like strawberries (easy to grow hydroponic) and cane fruits like blackberry and raspberry (which can be grown with little water and reproduce with ease).

Conclusions:

A lot of this research is already done. If you have the space and resources for hydroponic gardens, you can choose from a wide variety of plants and easily make a healthy and varied diet. Small animals and non-animal protein sources aren't hard to incorporate. And you can even have some trees and parks. You might choose some soil-based plants or animals for variety, and as a way to recycle your plant and animal waste. Add in your original thought of bamboo for construction and food, and you're pretty much set.

I would like to add: Algae and bacteria can be used to produce most needed macro and micro-nutrients and can be easily adjusted by genetic engineers.

Insects and mushrooms can be used and they are efficient way to re-cycle waste.

Texture, consistency and flavors can be engineered by food-tech to make it less like the Matrix porridge.

For plants: What Can You Grow Hydroponically

How would your diet look like? Well people like diversity and it is good to make people on flying-can more happy. Better have an efficient diversity so that you are both efficient and safe from mishaps and your passengers can have a choice.

I would grow spices some vegetables and salads, beans and rice in the hydroponic farms.

Produce a mass of protein, fats, carbohydrates and vitamins with algae and bacteria. Use as an addition to first and supplements.

Use some insects and mushrooms as part of a waste re-cycling.

Consider your generation ship as a taxi for any animals/plants/fungi etc.. that you would like to feature in the new world.

As it is a generational ship, those that arrive won't be those that left so an important aspect will be to literally train the children in how to handle wildlife for their benefit after terraforming the new world.

It would also be beneficial to transport organisms that will provide environmental services. This makes scaling out water purification, air cleansing, plant pollination, soil aeration, etc... without the need for machines that require hard to obtain resources.

These would need to include grasses, trees, vines, kelp, fish, molluscs, sea slugs, cattle, horses, birds, bees, fungi, etc... Take a look at the various biome projects for an idea of the variety needed for a stable eco system.

Additionally a terran biome would help alleviate certain health-issues with your colonists. Needs like helping to produce Vitamin D by exposure to Sun like light, training the bodies immune system to handle irritants, and providing stress relief.

Admittedly on your space ship the biome will likely be maintained at a minimum due to space efficiencies, and may not provide 100% of the food needed by the colonists.

Many leafy, and tuber based plants can be grown easily in hydroponics at scale. Many of them will grow fine in low-g environments. Kelp and various water plants are also easily grown in bulk, possibly helping with treating water. These will provide the bulk of minerals, and micro-nutrients needed by your colonists.

Protein and fats could be sourced from plant crops like soya beans, lentils, and lupin. However they can also be easily obtained in bulk from various insects like worms, crickets, and ants. Depending on the water system attached to the ship some aqua-culture for fats and proteins may be possible, but you will have to deal with water-quality issues. A terran biome area on the ship could provide such filtering along with careful selection of the farmed aquatic species.

The most important part of feeding your colonists will be supplying a variety of food rather than a few specific species, this increases the likelihood that they will receive sufficient nutrition. This will also help to safe guard the food supply due to a mismanagement, an accident, or a bloom in the population of some pest.

Tall plants and trees are completely out of the question: they don't do well in hydroponics, and unless you are flying in WH40K type monstrous cathedral ships, growing space is gonna be a bitch.
Any plants which require large quantities of water, like paddy, are too wasteful and thus, cannot be used.
Your best bet would be to not culture any higher plants at all. Fungi, like yeasts and mushrooms are highly nutritive, and take up comparatively less space. Better place some of that handy cloned meat in a nice, warm, humid environment and have some spores handy...
If you insist on having some plants for variety, spice olants would be a good bet, as your astronauts will need some seasoning. Plus, they are hardy plants and require very little processing. Beyond that, soya bean and other oilseeds, millets (require some processing, but are hardy) are ideal.