start simple and expand from there.
I recomment, as most will, that you start with a simple deep water culture system and grow tomatoes. maybe some herbs if you're concerned about having enough light.

I started with a hybrid aero/nft system. A couple of 4inch diameter plastic tubes, some quarter inch tubing, 1/2 inch pvc with holes drilled for sprayers.
The whole setup cost me about a hundred bucks. The biggest cost was the $80.00 pump.
I've tried DWC in a bucket. bucket, net pot, aquarium pump, airstone and tubing all bought new will cost you around 25 bucks.
I haven't had a lot of luck with the dwc system. I have 2 buckets with 2 plants in each one. root rot seems to be more of a problem in it than it is in my nft system. I've lost 6 plants to root rot in the dwc buckets.

DWC is easiest and cheapest. You should learn fundamentals of growing plants in hydroponics before moving to advanced systems

My opinion the difficulty of common systems is described by the following:

DWC With DWC easiest, Aero most difficult. Aero in fact really isn't hydroponics as the roots hang in air rather than water, but for the sake of simplicity I just group it with hydroponics.

Starting easy will allow you to learn about pH, EC/PPM, oxygenating water, how changing reservoirs and nutrients works and how often to do it, and also plant symptoms/stresses in hydro (which can be much different and come about much quicker than in soil).

I would add "to waste" there before DWC, ethno.

Drain "to waste" isn't an actual hydroponic system. Both NFT and aeroponics, for example, can be drain to waste. Its more of a descriptor or a choice of how to use the nutrients in a system that is usually recirculating.