If at all possible using the closet is 1,000 times better to grow in over that dresser,your going to have serious heat problems & no amount of computer fans are going to be able to control temps enough for a no problem grow.
Even with air cooled lights the light itself emits radient heat,this heat cant be extracted via air cooling the hood,it needs to be exhausted from the area,even a 4 inch duct booster fan might not be enough but for sure those computer fans wont cut the mustard,you should keep temps below 80 degrees at all times,between 70 to 78 is prime.
Space is going to be an issue as well,the plants will prefer more room to spread out & be more comfortable if you will,crowded plants are not as happy as plants with room to grow.
Now you have humidity concerns,your putting a dwc in an enclosed area,humidity levels are going to rise much more than what they would using the entire closet,plants feel exactly the same way you & I do about humidity,when its hot & humid we humans are miserable as fuck,we dont think as clear,dont do our jobs as well ect ect ect,mj plants are the same,they produce far less bud weight the more uncomfortable they are.
High humidity coupled with crowded plants also causes a dreaded condition known as powdery mildew, its bone white & will cover the entire plant surface,on top of all the no brainer issues associated with mildew/mold it can slow or stop all bud production,the white mildwe covers leaf surfaces & blocks the plants ability to absorb light,this stops photosynthsis,without that the plant cant process its own food,shoe horning a dwc, plus plants into a dresser is only going to seriuosly increase the risk of mold & mildew.
Water temps in the rez are another issue,as you have hopefully read or learned from the hydro shop water temps should be kept below 72 degrees,jamming all that stuff in a dresser surely isnt going to help keep the rez cool,no matter where you grow if you are not using some form of rez cooling system you need to cover the entire rez with white panda plastic,this will repel any radient heat & will block light from infiltrating the rez & causing alge to grow.
For your 1st time out you should be doing everything in your power to making sure every condition of the grow where you can control is set up so its best for the plants, with the least chance of issues that can cause failure.
Running a hydroponic grow in a dresser will at the very least double the chance of serious heat/humidity/mold & mildew problems,if not tripple.
Also you MUST have a ph meter,if you are using bottled water,or running reverse osmosis,or at the very least you know the ppm of your tap water you can grow successfuly without a ppm meter,just pick a fertilizer company who's products come with a very well thought out & self explainatory feed chart such as General Hydroponics 3 part system,if you follow the chart to the letter a ppm meter will serve no purpose until you learn more after a few more grows.
Also for a ph meter i strongly reccomend the Hanna Growcheck hand held unit,its a probe type meter with an easy to read LED screen,the probe is 12 inches long which helps in reading the ph,its also a SINGLE POINT CALABRATION UNIT which means it only uses one point of measure when recalibrating the unit,other growers will argue that dual point calibration units are more accurate but ive found that to be untrue & unfounded,i own several dual calibration units as well as the single point Growcheck unit & i find the Growcheck to be equally reliable & accurate.
Recalibration with dual point units requires the user to buy 2 seperate chemicals as in ph 4.0 & ph 7.0,the user then enters a set up menu & follows a series of prompts from the menu,then when the prompt tells the user he has to switch chemicals & repeat,a total pain in the ass plus the expense of constantly buying ph 4.0 & 7.0.
With the single point Growcheck you only buy one small bottle of 7.0 one time & never again, even if you run out,when you calibrate the Growcheck there is no programming menu,no pain in the ass prompts to follow either,you simply push the only button on the unit which is the ON button,then stick the probe into the 7.0 solution,if the reading is not exactly 7.0 there is a little knob on the unit you turn with your fingers,just turn the knob to the left or right until the meters LED shows 7.0 & your finished,the entire process takes about 30 seconds,with a dual point meter its 5 minutes or more.
Then if your a cheap ass like me you take your freshly calibrated meter & measure the ph of a new bottle of pure bottled water,write the ph value of the water on the bottle in permanent marker then store the water in a dark cool place,now when you need to recalibrate your meter you use the water as your control reference saving you money & time,you cant recalibrate any dual point meter in such a way,the Growcheck is the most user friendly meter on the market & something you need to grow hydroponics,if not the Growcheck you MUST have some kind of ph meter & cheap litmus paper tests ,or swimming pool test kits will not work.
Use the closet & you will have an easier time of it bud.