-During the first month you want every soldier to have at least 6 or 7 health to avoid getting one-shotted (most aliens during this period do either 3-5 or 4-6 base damage, flank crits will still kill you, so watch out)
-First research projectshould be xenobiology (necessary to start getting scientists), after that most people recommend rushing to beam lasers and advanced beams (for laser weapons and laser cannons for your interceptors), then rush advanced body armor and start building carapace. This should give you a decent air game, decent firepower and decent survivabilty for a while.
-Take your best troops on difficult missions, on easy missions bring some weak troops and some good troops in case things go bad.
-build lots of interceptors
-Look up the different ufo types and alien mission types on UFOpedia in order to figure out what you need to intercept. Some people will suggest ignoring scouts but this is a bad idea, ignoring a scout will not only increase panic over the country but also has a chance to spawn a fighter or destroyer to shoot down your satellite.
-Go on every terror mission if you can, even if you lose every civilian you are better off than you would be if you had just ignored or aborted.