How can I master the oven temperatures at which to cook things and corresponding cooking times without having to remember them specifically for each dish? Are there some charts anywhere on the internet, for instance in gif format?
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What you're really trying to do is add a measured amount of heat to your food in order to achieve the effects you want: in the case of e.g. a roast chicken, crispy skin and safe but juicy meat. As noted by Erica there is comparatively wide band of temperature in which this will work, so why not measure the temperature where it matters?
Buy yourself a digital thermometer. America's Test Kitchen has rated ThermoWorks as one of, if not the, top brand. A 'Chef Alarm' by TW will cost you about US$50, and consists of a probe you stick into the food, and a digital reader. It will make more of a difference to your meat dishes than anything else. Roast meats at around 210C as a base temp. This will seem pretty high, but will ensure you get a crispy outside while the inside cooks, and you can always modify once you see how your oven behaves. Chicken is cooked internally at 70C, pork about 65C, lamb or beef at 55C. You can even set an alarm on your unit to tell you when it's done. No more guessing - ever. In terms of veg, see a nice summary (conveniently, all cooked at about the same temperature too) at ChefSteps: https://www.chefsteps.com/activities/tips-tricks-perfect-roasted-vegetables
Most braises or casseroles will go in at about 150-170C for several hours depending on the thickness of the meat. The point in slow cooking to break down tough collagen into tender and tasty gelatin. For a great, instructive and short video on understanding the difference between tough and tender cuts (and why you can use the same techique for a shoulder of pork or a shoulder of lamb): https://www.chefsteps.com/activities/decoding-tough-and-tender-cuts
Oh - and cakes always seem to be cooked at about 180C. No idea why but most recipes seem to be written for that temp.