The lighting you can use will depend on whether the plants are close enough to a window to get natural light as well. Plants mostly, but not exclusively, use the blue and red wavelengths, so when the plant is near a window you can use cool-white and/or warm-white fluorescent tubes because the natural sunlight will provide more red light to balance the mainly blue from the fluorescents. You need for the lights to be bright enough, and close enough to the plants, for sufficient light intensity that the plants don't flop. You might want to check out these two articles if you're not familiar with growing plants indoors under lights:
DogsnDaylilies, the second of the above says "fluorescent tubes listed as white or daylight are less desirable for indoor plant growth". I haven't grown under lights for some time but used to start all our vegetable seedlings under them and always used cool-white as far as I recall, maybe combined with warm-white because that's what used to be recommended. I've never used "grow lamps" because I have always been able to place the plants near a window. Years ago it used to be said that grow lamps didn't have enough light intensity but I think they may have improved since then. Still for seedling growing where there is some natural light it would probably still be cheaper to go with cool-white - some people use a combination of cool-white and warm-white as mentioned above. I won't go into LEDs or any other alternatives because I've never tried them.
Re K-cups I, think they would be too small to keep daylily seedlings in for long but they'll likely tolerate it if you can keep up with the watering and fertilizing, daylilies are pretty tough. If you don't grow them under optimum conditions, though, you don't gain anything by starting them early other than something to do in winter
Picnic drinking "glasses" from the supermarket are an inexpensive alternative.
I'll post a picture below of one of my experiments to show you how much root growth you might expect by one month after germination - these seedlings were started in plain sand, in a shallow container, and had not been fertilized so not optimum (it was for a germination experiment):