Hi Josh, interesting project. First a greenhouse, look a my web page for the local chapter for a
greenhouse. The best material for an inflatable greenhouse on Mars is PolyChlorTriFluoroEthylene (PCTFE). That's sold by a few brand names, 3M used to sell it as Kel-F but they stopped making it in 1995. Now a Japanese company makes it but that have a brand name for all fluoropolymers so you have to use PCTFE. Honeywell sells it with 2 brand names: Aclar targeted at the pharmaceutical industry (blister packs for pills), or Clarus targeted at aerospace and military. They're the same thing but I suspect Clarus is more expensive. Plastic film just 2 mil thick will have a significant safety margin and it'll handle cold 100°C colder that the coldest spot of the Martian south pole in southern winter. But you want to land near the equator, within tropical latitudes for warmth (relative). Also pick a spot below the datum for radiation protection, and a spot close to a source of water. Permafrost could be melted and filtered to give water, you don't need a frozen lake or liquid aquifer.
As for life support: I strongly recommend a recycling chemical/mechanical system during the trip to Mars, then keep it as a backup to the greenhouse. Biosphere 2 found excessive consumption of oxygen by microbes breaking down plant matter they buried in the soil. You don't want some other surprise from the greenhouse depriving you of oxygen. Life support requires a few parts: dehumidifier, reverse osmosis filter for the urine collection tube, also RO filter for dehumidifier effluent. Another RO filter for wash water. Water electrolysis by proton transport membrane to make oxygen. Regenerable sorbent to scrub [tex]CO_2[/tex]. Human metabolism makes water from oxygen and carbohydrate, but the electrolysis tank will consume twice as much water; so you need a Sabatier reactor to combine all of the hydrogen from electrolysis with half of the [tex]CO_2[/tex] from the scrubber to make methane and water. That'll make the other half of water that electrolysis needs. There will be some losses but a direct [tex]CO_2[/tex] electrolysis system can make some oxygen to replenish oxygen, and surplus oxygen so you can turn down water electrolysis to let water accumulate. Direct [tex]CO_2[/tex] electrolysis is very power hungry so you want to use it as little as possible, but it replenishes loss of both oxygen and water.
A chloroplast system is great to produce starch paste, and you can grow yeast in that for protein, but in-vitro chloroplasts have a limited life span. I suggested bringing bags of chloroplasts in liquid nitrogen for the trip. Hopefully each bag will last 6 months, but that's only a hope; I have no data to base that. On the surface of Mars you'll have to grow pea seedlings to harvest new chloroplasts. You cut off leaves 2 weeks after germination, grind them and centrifuge to isolate chloroplasts. The centrifuge is about the size of a blender, and the lab procedure calls for a fancy (expensive) hand immersion blender sized for a test tube. I suspect a professional restaurant hand blender will do, just use a beaker instead of a test tube. But you will need chemicals: percoll, hepes, NaOH, sorbitol, acetone. There are a few different protocols, each with slightly different chemicals. I can tell you how to make NaOH and acetone, but right now I don't know the others.
Size: according to "The Case for Mars" paper back edition page 89, a piloted mission to Mars using [tex]H_2/O_2[/tex] fuel will require 40.6 tonne throw to trans-Mars trajectory to land 25.2 tonnes on the surface. Proton 8K82K/11S824F can throw 6.220 tonnes to a trans-Mars trajectory. That should be able to land 3.86 tonnes on the surface. Energia with EUS can throw 35,680kg to C3=0, 31,091kg to C3=10, or 17,446kg to C3=50. A manned mission to Mars will use C=15 so interpolating I get 24,207.5kg to TMI. Then calculating landed mass I get 15,025kg (15.025 tonnes). The problem with Energia is its vehicle assembly building roof collapsed in May, 2002. That will be expensive to repair. The price quote was $60-100 million to restore infrastructure and $120 million per launch including EUS, but that was in 1994. It would be more expensive now.
You could use the big version of Magnum that NASA is considering for the Moon. It would be big enough, but American rockets built by major aerospace companies for NASA tend to be very expensive.
A greenhouse can be made relatively light. Use a double layer PCTFE bladder with spectrally selective coating to block UV and control heat loss, and an aluminized Mylar curtain inside to reflect heat at night. Extract argon from Mars air to fill the gap between bladder layers (argon conducts less heat than air) and shovel in Mars regolith to weigh down the bag. Also use hold-down straps to squash it into an oval. An Earth greenhouse uses plant trays to hold soil, raising them up for ease of gardening, but you could plant at ground level like a vegetable garden. Growing in ground level soil requires something to prevent a shovel from puncturing the air bladder under the soil. PCTFE is probably strong enough that plant roots can't pierce it, but a gardening trowel could.
Most importantly you need a really, really good power supply. For the Mars Homestead Project I calculated life support power requirements for a 12 person base. I based it on life support equipment built by Hamilton Sundstrand for the US Habitation module of ISS, so it is flight equipment. Since that equipment is sized for 4 astronauts I multiplied by 3 for Mars Homestead. For your needs I would divide the Mars Homestead results by 12. That gives:
toilet: 31.25 watt peak, 0.005989583 kWh per day
water processor: 76.25 watt peak, 0.1167 kWh per day
oxygen generation: 144.167 watt continuous
[tex]CO_2[/tex] removal: 21.583 watt continuous
dehumidifier: 50 watt continuous
circulation fan: 26 watt continuous
Sabatier reactor: doesn't use energy, net heat producer
This adds up to a total of 246.860677 watts just to run life support. Then add lights.
I find 14 watt compact fluorescent light bulbs have the same light as a standard (cheap) 60 watt tungsten light bulb. The straight (not twisted) compact fluorescent lights from GE have a very nice spectrum. The spirals from Philips are easer to find and slightly cheaper, but have a slightly odd spectrum; some white paint looks slightly pink. I use a single GE 14-watt light bulb in my bathroom, but two bulbs in my home office. If you use compact fluorescent, use a modular fixture. That has a separate ballast from the bulb, so you can develop a ballast that uses DC power from solar panels. Modular bulbs also tend to last longer: 10,000 hours instead of 8,000 hour for GE bulbs or 6,000 hours for Phillips bulbs. White LEDs tend to last 10 times as long as compact fluorescent and use even less power, but expensive bulbs and you need a lot of really tiny bulbs. Considering the cost of transport from Earth, white LEDs are worth it. Budget 14 watts to light a single small room.
The greenhouse can use ambient light, but there will be many pieces of equipment that need power. Direct [tex]CO_2[/tex] electrolysis consumes slightly more than twice as much power as water electrolysis, and that doesn't include power to heat the gas to 900°C. I don't know right now how much power you'll need but it's significant. You would do well to reduce consumption to 1kW, 3kW might be more realistic. Ultra triple junction solar panels from Spectrolab are space rated, they produce 350[tex]W/m^2[/tex] beginning of life for panel area >2.5[tex]m^2[/tex] and mass 1.76[tex]kg/m^2[/tex] for panels with 3 mil Ceria Doped Coverslide. Efficiency is 28.3% beginning of life, 24.3% end of life, so expect 300[tex]W/m^2[/tex] end of life. To produce 3kW you would need 10[tex]m^2[/tex] of panel massing 17.6kg. That doesn't include substrate, you would need some sort of backing to support it and a frame to track the sun. Sunlight will only be up 50% of the time, so budget 500 watts during the day to run life support and recharge batteries for life support at night. This only gives you 2.5kW during the day to operate equipment for mining, refining, and manufacture.
NASA tried to support a single test subject for 90 days with a greenhouse. It was part of their advanced life support project. They used hydroponics with bright lights 24/7 and multiple levels of plant trays. You would use soil agriculture with a single layer (ground level) and ambient light. You can use mirrors on either side of the greenhouse to reflect more light, raising the light level to equal Earth. That would be most efficient but would require more floor space than NASA's experiment. Based on
NASA's calculations growth area for 6 astronauts is 66.9[tex]m^2[/tex] so assume 11.15[tex]m^2[/tex] for just you. If you put a 0.5 metre wide isle down the centre, the greenhouse floor would be 3.5m wide by 3.71667m long. If growing area is 90% width of the ellipse of the pressure bladder, it will be 12.5kg of film. That assumes the ellipse is 2.5m high at the centre, subtract soil depth to get head room. Add mass for door, airlock, etc.
::Edit:: Correctin, you can't divide peak power for the toilet by 12. A toilet is a toilet, so peak power can't be divided. However it'll be used less often if there's only one person so the average power use per day is correct. That means total power required is still the same.