I would focus on the video usage...any quality light that is usable for video will suit for stills. I don’t do a lot of video currently other than producing some streaming web shows, but previously did a LOT of work in that field as a lighting director and editor. Best options I’ve found are some of the LED panels out there. The set I am using has two sets of bulbs so color temps can be more or less tuned. Challenges are that they generally are not super high output and tend to be small and therefore specular in quality. Very hard to get them to produce soft, flattering diffuse light unless you move them in very close. An upscale and preferable option would be a Kino-Flo fluorescent system, which solves both of those issues. I personally would try to avoid using a hot bulb - photo flood or halogen, again for continuous light because of heat and power consumption.
For my my web shorts...I’m using two 12”led panels about 60” off the subjects for main and fill. Background and key lights are actually the modeling lights off of my studio strobe lights (PCB Einstein’s).