I'm in love with mineral powder because it's magic. It's not hardcore e.g. that stuff that's basically wipe-on plastic for photoshoots or video and whatnot, so it might not be right if you want a super-perfect look for being on cam. However, if you're looking for a REALLY simple and minimal (and skin-kind) solution for just a bit of shininess, pop "mineral powder flawless matte" into Google - the first result is the one I use on no-foundation days.
It's white in the pot but goes on colour-less (so no shade matching, woohoo) and just matte-ifies any shine on my face from the generous amounts of moisturiser I always use. It lasts about 6 hours and then I'll either top it up or I'll be home again by then and will therefore no longer give a toss about the texture of my skin.
You can order samples from their website, too, so you needn't spend more than a couple of quid if you just want to test it out. Or, of course, there are other mineral makeup brands that you can check out in department stores if you want to compare price etc.