I have grown beans, tomatoes,peppers and strawberries successfully in a drip system, I usually start the seedlings in soil and then wash off and transplant in hydroton with very good results. I have not grown cucumbers but I believe this is possible. I see a lot of people using rockwool successfully but I have found ( and it is only me) that rockwool holds the moisture even in between waterings. The cost is fairly high but then that is only me and I suppose after others read this posting some will say nonsense and they could be 100% correct. After 40 years of growing hydroponically I have found something that works for me and I will stick with it. NFT is the only system I have not used but I believe strawberries, beans, and especially lettuce and asian vegetables could be very good. I grow most of my larger plants, eg tomatoes, peppers, egg plant etc in my ebb and flow system , and my leafy vegetables in my DWC trays. At present my strawberries have pride of place in my drip system.
The attached photo was last year when I grew Thai Tomatoes in my drip system which went very well.
I was growing Kang Kong a chinese vegetable at the same time as you can see in the back of the photo.