One of the basic necessities not yet mentioned is clothing.
Most clothing is made, not surprisingly, of cloth. That in turn is made of woven threads, which are made either of plastic, animal hair or plant fiber.
I'm going to eliminate animal fibers simply on an efficiency basis. The varieties of animals that are raised for fur (sheep, rabbits, goats, yaks) can also produce meat and milk, but are much less efficient than purpose-bred varieties. Sheep are probably the best all-round performers (~5.4kg wool per animal per year eating about 2kg/day of feed), but we can still do much better than that. Of course any incidental fur, skin, etc. will be used for filling, lining, leather and such, but we cannot assume there will be enough of that material to clothe everyone.
Read on for the rest. This turned out to require a lot more growing space than I would have thought, 10.26m² per person.
Plastic has many benefits. Some routes to plastic production don't involve living organisms as a bottleneck. Others use byproducts of food production. Depending on the choice of plastic the resulting fabric can be quite strong, durable and chemical-resistant. Dyes can be incorporated directly into the fibers for simpler, more durable coloring. Plastics can also have drawbacks like static buildup or melting, and tend to be degraded by UV exposure.
On Earth, the main clothing fibers are nylon, polyurethane (as Spandex), acrylic, rayon and polyester. Nylon and polyurethane are fully synthetic, typically at the end of a long chain of processes that start with benzene. Acrylic is also fully synthetic, most commonly encountered as cheap knitting yarn. Rayon is a cellulose polymer that typically starts life as wood or bamboo fiber; it is considered semisynthetic even though it is just as heavily processed as nylon. Polyester refers to a family of plastics, some of which are found in nature. Notable polyesters include PET (PET as Dacron, BoPET as Mylar), Vectran and PLA.
Notice that none of those are my favorite plastic, polyethylene. I suspect PE fabric for clothing would be uncomfortable, with no stretch and a slightly oily feel. Excellent as an outer layer in a protective garment but terrible for underwear.
Plant fibers also have many benefits. Softness and durability are at the forefront. Natural fibers tend to withstand flexing better than synthetic fibers. These tend to char rather than melt. They also have a softer feel. On the other hand, natural fibers are more difficult to dye and can be more labor-intensive to produce.
On Earth the main clothing fibers are cotton, flax (linen) and hemp. All three are grown for their fibers and seeds; the seeds can be eaten, milled into flour or pressed for oil. All three are suitable for hydroponic cultivation, mechanical harvesting and mechanical processing.
Regardless of type, the various fibers are spun into yarns. Often the yarn is composed of several different fibers in order to combine desirable properties. For example, it is very common to include a few percent Spandex with cotton or nylon to produce a yarn with some elastic response.
From yarn, some types of clothing are knitted directly. Machine-knit sweaters and socks are common. Other types require that the yarn is woven into fabric, which is then cut and sewn. One key variable is the weight of the fabric, typically specified in ounces per yard or grams per square meter. I'll be using GSM / grams per square meter. For example, a thin t-shirt might use 100 gsm material while a resort hotel might offer super-thick 800 gsm bath towels. I've used values below that are in the middle of the range for each fabric type.
Fabric amounts are handled oddly in the US. People specify some number of yards of length, but often fail to mention that it's not square yards. Fabric is typically sold in widths of 45" or 60" (sometimes 32"). If a pattern calls for 2 yards of 45" fabric, that's actually 2.5 square yards. I've listed values below in square meters. I used a variety of sources; there was one excellent sewing blog with tables for the first three items, then I found a pattern for coveralls. For the bath and bedroom items I used actual dimensions, added an allowance for hems and converted to metric.
Typical fabric requirements:
pants, 1.5-4.2m² (2.5m² avg.) x 250gsm = 625g
shirt, 0.7-3.4m² (2m² avg.) x 150gsm = 300g
dress, 1.3-7.7m² (3m² avg) x 200gsm = 600g
coveralls, 4.3-6m² (5.3m² avg.) x 350gsm = 1855g
sheet (queen): 6m² x 150gsm = 900g
sheet (full): 5m² x 150gsm = 750g
blanket (single-layer fleece): 7m² (90x110"/ 230x280cm) x 350gsm = 2450g
quilt (2-layer without filling): 14m² (90x110"/ 230x280cm) x 200gsm = 2800g
pillowcase: 1.4m² x 150gsm = 210g
napkin: 0.4m² x 200gsm = 80g
towel (face / washcloth): 0.1m² x 350gsm = 35g
towel (hand): 0.4m² x 350gsm = 140g
towel (bath): 0.9m² x 500gsm = 450g (also worth a read)
(Edit 2015-11-11: I found another link with some citizen-science that provides measured values for clothing. A women's outfit was 0.65kg and a men's outfit was 1.1kg. This suggests my clothing allowance below is high but not unreasonable. I also recommend Rob Cockerham's site on a personal level; lots of interesting content.)
Let's assume each person has a full set of bedding and bath linens, a blanket, a napkin and one week of clothing. The linens come to 20.2m² of various weights, 4.865kg. Clothing depends a lot on the person's size, preference and occupation; I will add the first four values and divide by three to get an 'average' mass for a day's clothing. This is likely to be high as I doubt that a third of the crew will need heavy denim coveralls for daily work. Still, that comes to 29.9m² or 7.887kg for seven outfits. That's 12.75kg in total; add a bit of leeway for knits and undergarments (~1.5kg), thread, sizing, etc. and call it 15kg per person. Specifics may differ; I'm assuming a full-size bed and all single people. A couple could use the same sheet and bathroom set. A more regimented facility might use Navy-style hot bunks and hot air drying after bathing to cut most of the linens. I suppose wealthy tourists might want more amenities.
These things wear out. Socks and undergarments typically last perhaps half a year. Outerwear lasts 1-3 years depending on circumstances, so let's use one year. Bedding and bath items can last many years, but let's call it three. Heavy-duty work outfits like denim coveralls might last a decade or might wear out in three months; call it one year. On an annual basis using these numbers each person needs about 12.5kg of replacement fabric. These estimates are a bit conservative; many people replace their clothing far less often than this and only when they are actually worn through. I assume that the 'replaced' garments may not necessarily be discarded and people may simply build up a wardrobe over time. Sufficient space could be available to store 2-3 weeks worth of clothing, while worn or damaged pieces would be used as rags or as fiber sources for filter paper.
Let's look at yields. I simply don't have enough information available to predict the material requirements for plastics, so this will focus only on natural fibers.
Cotton can be grown at 1000-1500 lb per acre in open fields. In a hydroponic environment with no pests and tight nutrient control it should be possible to significantly exceed that mark, but let's use 1500lb/ac for this estimate. 4047m² per acre gives us about 0.37lb per m² or about 168g/m². Estimates range from 150-180 days for a growth cycle, so let's use 165 days. That works out to almost exactly 1 gram per square meter per day. Each person needs 34.25 grams per day, which would require 34.25m² per person. If we use a record yield of 6.31 bales per acre, that would be 3,536kg/ha or 354 grams per m² or 2.15g/m² per day > ~16m² per person. Seed production is about 1.62 x cotton production, or 3.48g/m² per day.
Flax can be grown to yield over 1800kg/ha or 186g/m². Growth cycle is 90-125 days (in Canada), so we will use 108 days. That gives 1.72g/m² per day or 19.89m² per person.
Hemp has yielded 6 tonnes of fiber per hectare or 600g/m² (again, Canada). Growth cycle is 70-90 days for fiber only (80) or 110-150 days (130) for dual crop. Using the dual crop number we get 4.62g/m² per day or 7.4m² per person. Seed production is about 0.7g/m² per day.
Based on those numbers it sounds like a mix of 2:1 hemp and cotton would be ideal. That would be 4.93m² per person of hemp and 5.33m² per person of cotton to produce a total of 12.5kg of fiber. The process would co-produce about 1.25kg of hempseed and 6.77kg of cottonseed plus another few kg of plant waste.
It's worth mentioning that the record land yields tend to be twice the high averages, if not more, for most crops; even so, hydroponic methods can often surpass the record yields simply by preventing stress. Crops that have not been optimized for performance (like flax and hemp) have the potential to double or triple their yields given a dedicated breeding project. Have a look at dwarf rice and wheat yields vs. the varieties that existed before the 60's for an example of this in action. In other words, within a decade any number I post here will be obsolete as long as someone is actively developing the potential of these species. I think a combination of longer 'useful life' assumptions for clothing and improved hydroponic yields could cut the required area down below 3m² per person. That research and breeding could be applied to commercial crops on the ground, providing improved incomes for farmers around the world.