The staple item of the diet of 16th century sailors was the hardtack/ biscuit. It was a specially prepared double baked piece of wheat bread, making it very hard and very durable. It was usually baked on land in specialized bakeries (for example Seville and Lisbon had dedicated Royal controlled bakeries for baking biscuits for their ships) and distributed in large amounts to ships.
Shared provisos onboard usually also carried nuts of all sorts like chestnuts and almonds and dried fruits like raisins and dried plums quinces, and figs. Jams were also sometimes carried. From vegetables you could find onions, lentils, beans. Rice and cheese were also common.
Meat and fish were highly important parts of the diet. Ships were usually provisioned with dried meat and salted fish, but many also carried live animals onboard like pigs, goats and even cows, which they would kill and eat when necessary. Sailors also used to fish in their free time, but they really couldn't count that they will catch anything.
Ship stores would also be equipped with various extras, necessary for cooking, like oil, vinegar, sugar (which was more expensive) and honey (which was cheaper).
All men onboard also had a designated amount of private items they could carry on (size depended on rank and importance) and many would use this to bring extra food, supplementing their diet.
In Iberian 16th century merchant ships it seems there wasn't a common cooking galley, but each man cooked for himself, on deck. Men could and commonly did team up and cook together, but sharing food wasn't expected by itself. The food, especially the hard biscuits, was usually mixed with fresh water and cooked. This was both the simplest but also almost necessary, as some of the dried food was to hard to be eaten without some way of loosening it.
We have records and estimates of how much each sailor was given of common rations.
In 1606 Instruction of Pedro Fernandez de Quiros to his second in command instructed following about the ration sizes in his sailing in the Pacific:
The ration to be served out each day to each person on board, whether receiving wages or not, is 1 1/2 Ibs. of biscuit, 1 Ib. of meat, 2 oz. of bacon, 1 oz. of pulses, half a gallon of water for drinking, and sufficient for cooking. On fish days the ration is to be one fish or (if it is large) part of one, 6 oz. of pulses, a measure of oil, another of vinegar ; biscuit and water as on meat days. If there is no fish, 4 oz. of cheese is to be substituted. As regards extras, what appears most convenient is to be done, always seeing that there is no pretext for complaints, and considering that there is much time and a long voyage before us.
And we have a modern historian estimate of the food rations 1590s Portuguese 500 ton carrack sailing to India
| Item | Amount |
|---|---|
| Hardtack (biscuit) | 989 g per person per day |
| Wine | 1.006 L per person per day |
| Meat | 250 g per person per day |
| Fish | 5 fish per person for the whole trip +what you catch |
| Olive oil | 0.435 L per person for the whole trip |
| vinegar | 0.796 L per person per week |
| Water | 2.738 L per person per day |
| Salt | 0.3 L per person per day |
| Sardines | 5.387 kg per person for the whole trip |
| Chickpeas | 0.5 L per person for the whole trip |
| Almonds | 0.36 L per person for the whole trip |
| Plums | 0.36 L per person for the whole trip |
| Lentils | 0.36 L per person for the whole trip |
| Mustard | 0.07 L per person for the whole trip |
| Garlic | 2 braids per person for the whole trip |
| Onions | 2 braids per person for the whole trip |
| Sugar | 325 g per person for the whole trip |
| Honey | 325 g per person for the whole trip |
For more overview of the total supplies brought on an expedition we have very good list of supplies carried on Magellan's circumnavigation of the world, in this book, pages 331, 332
For combating scurvy, we have records of 16th century Portuguese knowing that lemons, oranges and citrus fruits do cure scurvy (they have either knew this from before, or gotten info from Muslim traders once they reached in the Indian ocean) but, honestly, on board there wasn't much they could do when scurvy set in, other then try to find land and fresh fruits to give to the sick.
However, for your particular hypothetical situation, crossing of Atlantic e.g. from Spain to Americas, scurvy really wasn't an issue. Scurvy sets in 2-3 months after fresh food is cut out from the diet, and the Atlantic crossing was usually much shorter then that. As per this source:
In the sixteenth century, the journey from the Canaries to Deseada ordinarily consumed from twenty-five to thirty days. From Deseada the galleons steered an easy course southwest to Cape de la Vela, and thence to Cartagena, reaching the latter port six or seven weeks after their departure from Spain.
So the total voyage time from port to port was two months tops, from which only about a month was through open ocean, and the rest was sailing nearby land from which one could if necessary be supplied with fresh food or water.
The more complicated voyages were the route to India around Cape of Good Hope, and the crossing of Pacific from Acapulco to Manilla, both of which would take around 6 months by average, and on which scurvy and other bad conditions on board often decimated or even halved the ship crews.