I basically did and am currently growing with something along the lines of what you described. I am no DIY pro but I did manage to create my own DWC system. It was quite easy. I understand you wanted to do just 1 plant, mine however is 6. It a very thick plastic rubbermaid container and light penetration is minimal. The stuff you need to make this is
1. rubbermaid container (15gal) roughneck is the line = ~ 10.00 USD
2. 1 aquarium pump. Sold at any pet store or Wally world = 15.00 USD
3. Air stones and tubing . Again sold at pet store or Wally world = 4.00 total , air stones can be expensive but if you get the small .99 cent ones they do the trick. PROTIP= more bubbles in your res the better so if you can get afford a bigger air pump and air stones get them. Just make sure they fit in the res.
4. Net pots = you can take those small plastic dentist cups or small plastic dixie cups and poke holes in them at the bottom. Or order online. they are cheap and effective = 3.00 USD (pack of 25)
5. Expanded clay pellets or hydrotons. (while originally when I started growing I thought "I NEEDED" these to grow. When in fact these were not completely necessary. You can use any kind of small polished rocks. They do not retain water like the hydrotons do but they do help the plant anchor it self. That's what you are aiming for. SO you would have to go in and run some water over the rocks every day until the roots reach the res line. Some people raise the res level to the bottom of the net pot. This is a good method and alternative if you aren't able to spend time in the garden everyday. Aquarium rocks are inexpensive too about 5.00 for a big bag sold at wally world or any pet store.
6. rockwool is a good place to start seeds but if you have rooted clones its not necessary. I start seeded in paper towel then transplant germmed seeds into rockwool. That's probably the only thing you will need to buy off the internets. And they arent too expensive.
here are some pics of my setup. You will want to invest the most money in your lights and your ventilation if heat is going to be an issue. These are aspects of your grow where you do not want to cut corners and buy cheap replacements. I have seen some really good grow ops with great DWC setups and other forms of Hydroponics with some really expensive nutes but they went with a sub standard type of lighting. NOT ENOUGH LIGHT i mean and their plants suffer. I love CFLs but growing with them you have to keep them constantly at 1 to 2 inches away from the plants due to their lack of lumens. Also beginner growers mistake the actually lumen output of a CFL because the box that they came in is misleading. If you grow with a 250w MH/HPS you will have a bad ass plant to harvest with a DIY DWC. Since I have 6 plants flowering I have to use a bigger light. 600w HPS might be a little overkill but I am making it work.
Again I spare no expense on the lighting. In the flower room is a T5 6 bulb fluorescent light fixture. Really great for mother plants and vegging clones. In the flower tent I have a 600w HPS light.
I hope this helped and can give you some ideas.
Peace and positive energy to you.