Well I'm not exactly high elo but ill give my advice anyway, just take it with a grain of salt. First of all its hard to know exactly what to look out for in champ select since it is a lot about what pick you get. Bot lane is usually decided by the supports unless there is a huge disparity in range between the adc's, so if your pick early i would suggest picking more utility since its harder to counter a Jana then a Leona. In general I would say pick towards what your team wants to do rather then trying to counter the enemy. Usually team comps are either engage, poke, or split push. If your building engage then a strong front line like Braum, Leona would be really good, for poke your team will need disengage from you so champions like Jana and Nami work the best. If you are trying to run a split push comp then that usually means you will either want a disengage support or a pick support so Thresh, Jana, and Nautilus work well.
Game phase is all about recognizing what objective are available for your team. The general tier list goes Nexus(obv), Inhib/baron, turret, and dragon. The job of support is to set up vision IN ADVANCE of what ever objective your team is looking at taking. When your ahead this is easy since you can generally go where you want to get wards placed. When your behind it becomes harder since it's easy to get picked off. My advice is to try to concentrate your warding around a single objective. What i see a lot of supports do is try to ward every objective and end up with random small pockets of vision. Your vision should give you **CONTROL **of an objective not just vision of it. What i mean by control is that you can walk into dragon knowing if your enemy is stacking a brush because your wards already saw then entering it. A single ward in dragon pit isn't going to tell you this only wards around the dragon to see them entering it will. Everything else is mostly down to mechanics and hitting skill shots :)
GLHF