The simpliest approach would be to start the two year mission with all of the consumables you're going to need. A more complicated approach is to have recycling systems to reduce the amount of consumables to the lowest point possible. However, what happens if the recycling systems fail? Will safety considerations dictate that you have sufficient backup food, water, O2, etc to fly the mission without the recycling systems? If so, then why not save the weight and expense of the recycling systems?

Looking at it in a little more detail, I believe it makes sense to recycle when possible and practical. For example, according to this source, this was the consumable load on the Skylab station when it took off:

"Oxygen and nitrogen was stored in high pressure tanks as pressurized gas. At launch the oxygen weighed 2,240 kg (4,930 lbs.) and the nitrogen weighed 600 kg (1,320 lbs.). The total water supply for all three missions was launched with the habitat on the Saturn 5 launch vehicle. Estimated at a usage rate of 5 pounds per person per day, the total quantity of water that was calculated to be needed for the scheduled one hundred seventy-one mission days, assuming three astronauts would participate in each mission came to about 1,166 kg (2,565 lbs.), plus a little extra "just in case". At the time Skylab was launched, the water stored onboard weighed 2,700 kg (6,000 lbs.). Food was also supplied at launch for all three missions and weighted 670 kg. (1,470 lbs.). There was a two-gas pressure and distribution system that, once in orbit, supplied a mixture of 70 % oxygen and 30 % nitrogen. The oxygen and nitrogen mixture was supplied to both the OWS and the EVA's. The oxygen and nitrogen amounts to be added were determined by the total pressure and the oxygen partial pressure. Oxygen has a partial pressure of 2.48 N/cm2 (3.6 psia) while nitrogen had a partial pressure of 0.6 N/cm2 (1.4 psia) (NASA-2). "

So, let's look at those numbers and extrapolate them to a 4 person crew on a 2 year round trip to Mars.

Water: They estimated it'd take 5 pounds of water per person per day. If you have no recycling, then you'd need 14,600 pounds of water.

Food: They provided about 2.85 pounds of food per person per day on Skylab. For Mars, you'd need about 8,400 pounds of food.

Oxygen: They provided 9.6 pounds of oxygen per person per day on Skylab. For Mars, you'd need 28,060 pounds of oxygen.

Nitrogen: They provided 2.57 pounds of nitrogen per person per day on Skylab. If there was no recycling, you'd need 7513 pounds of nitrogen of the Mars mission.

All together, those essential consumables would weigh 58,573 pounds at launch. That's quite a bit of weight just for consumables. Keep in mind that extra weight is the enemy of spaceflight. Every extra pound at the beginning of the flight would require several additional pounds of propellant, storage tanks, etc. These things have the tendency to snowball quickly.

Using some proven technology, it should be possible to reduce that considerably. For example, the Russians used electrolysis to break down urine for oxygen. The system worked pretty well. That would allow you to take a waste product and produce a consumable. You might be able to cut your initial oxygen requirement by half or more with this technology. Or, you might use water vapor capture (from evaporation, respiration, and perspiration) to provide water for drinking and bathing. This could also reduce your water requirements considerably. Condensors and filters aren't exactly cutting edge technology.

Recycling food is more difficult. While soldiers have been complaining for years that field rations are little more than recycled food (in raw form), it'd be tough to expect astronauts to put up with that for 2 years. Growing plants onboard is attractive because they also absorb CO2 and give off O2, but what happens if you have a crop failure? I'd recommend trying to grow some plants, if for no other reason than providing something to do on the mission and some variety to their diets. However, I don't think it'd be prudent to depend on that for a substancial percentage of your food or O2 supply. Besides, once they're on the surface for months at a time, would it be a good use of astronaut time to tend to the plants?