I'd suggest giving a single 5 gallon bucket with a net pot lid and an air stone and pump before diving in with chillers etc... grab the necessary items (air pump, stone, hose, bucket and lid) and sit thag 5 gallon bucket with about 3 to 3.5 gallons of the same water you'd be using to grow with and set it up and let it run for a day or 2 in the intended grow area and see what your water temps range round about... if u can keep them around 70, 65-68 is ideal...but see how things pan out like that before busting a nut and buying a chiller... you will need one eventually if u decide to stick with it one way or another; a chiller of any sort is probably the most important item in any active hydro grow... dwc generally doesn't require it as people usually run bigger resivoirs in cooler areas like a nice cool basement floor, but it will be an inevitable and unreplacable tool if you do stick with hydro... I would personally stay away from circulating nutrients etc directly through the chiller as most hobby type chillers recommend but rather use stainless wort coils (used for making beer) and setup a resivoir specifically for water that circulates through a closed loop system via your chiller and a cheap general type hydro pump... if you ever expand you can just add a pump and wort chiller coil along with a thermostatic controller to let the chiller and pumps know when to go on and off which u can get on amazon cheaply...
I can explain the chiller concept a little better if u like but I think as long as your grow area isn't way to hot you should be able to do a grow without a chiller and probably build a diy 5 gallon bucket dwc setup for like $30 or less... probably way less... but it's tough to chill single buckets which why I say to hold off on the chiller until your sure your gonna stick with it... even if your gonna stick with 1 bucket/res, you shouldn't push nutes through the chiller because should any of you plants sitting in the nutes ever get root rot (which theoretically shouldn't happen if your chilling your water) or any other disease that can be passed from plant to plant will at best be a pain in the ass to get completely out of the chiller... this is why I'll never do the single chiller to a single res type system no matter what type of hydro I use.... if you keep your chiller on a closed loop, the water in that loop will never come in contact with your plants nutrient solution which is the best way imo... it's more complicated, more expensive, and will take up more space but if done right, be hard to improve upon...
Last and certainly far from least; keep all organic based products out of your dwc res if you decide to go for it... the last thing you wanna do with non-recirculating dwc (rdwc) is go with organic nutrients... I'm sure there are people out there doing it very successfully but it's hard to do and not recommended especially for a hydro newbie... I've grown soil for years before getting back into hydro recently because I did all the things I suggested you don't do; and I'll say that even with a fairly good know how of everything, there is still definitely a learning curve that you gotta get straight on before you start throwing cash at problems... you'll be out a whole bunch of $, spent more time suffering through headaches than need be so take it slow n give a bucket a single run before getting knee deep in $$$ hydro gear...
I will say after my days of organic soil which I was more than happy with but due to a move; my locale isn't friendly to bags of soil going in and having to store dirt as people are just too close and worse; nosy... so hydro is much better for my living arrangement now.... but I am enjoying the change of pace/way of growing in hydro but it took many years of truly getting patient before I could attempt what im doing now...
It's worth a try but start small and cheap for a taste before you go big and make sure it's for you...
As far as nutrient selection, method or whatever I'd suggest the Lucas method and at half strength to start without any additives as dwc doesn't need a very high ppm/ec, same for most hydro grows aside from drain to waste systems can be ran higher but 99% of the bottled recommendations are waaaay to high so keep that in mind...
Good luck, hope it works for you cuz I'm liking it myself...ask me if I feel the same when the summer months start hitting and I might tell u different but I'm glad I got the chance to try it again, but as I said it took years of derty growing patience to even be close to partially successful at it... I been going for a few months n still have kinks to work out but they're working out quickly now...