Try to get organic and get the ones that are not huge but at most medium size (depends on which type of root of course)...I always go for the medium-small, they tend to have much more flavor and taste better.
Keep in mind that if you don't like a root it MAY be a bad batch or a bad sort...for example I usually get delicious sweet potato thats a deep orange. Today I got sweet potato somewhere else and when I sliced it the color was a pale orange-pink instead, it had no taste! I cooked it to see if that would make it better but it still was crappy. So try to find a source of high quality organic and local veggies if you eat them.
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I had a sample of daikon at the store. It was juicy, crispy, and crunchy, without much flavor.
Radishes, on the other hand,
I do not recommend, They give me a headache.
Beets are excellent, and celery root is tasty....
Seems we have very different root tastes, daikon (at least the one I get) has a lot of radishy flavor which is good, when shaved it spices up a salad. I like it with carrots and red cabbage etc.
I eat the little red radishes in small amounts but have never got a headache from them, I like them with mayo
however they are not the best tasting roots IMO.
Some or the best to me are parsnips and purple-top turnips, yum.
Beets are not bad but again only in small amounts, and for some reason the taste or raw celery is a little creepy to me, so I can't really enjoy.
Carrots of course most people like, they are great, get the little organic ones with the green tops not the giant ones or 'baby carrots'.
Out of all the vegetables I love roots and cabbages the most, I would be sad without them.
I have only eaten cabbage as my vegetable for the past few days...still pigging out on sauerkraut we made, its got little shaving of carrot and carraway seeds, its both sour and spicy but its half-fermented-half fresh, I love it at that state. Sometimes the store bought saurkraut is too bland and soggy, and too sour without enough zest/spice )=
Anyone who likes saurkraut I recommend you to make your own