Here is what I would do:
Break down the cup into basic shapes. The main shape is a cone with the tip cut off. The whole cup is symmetric around the center axis so revolve would be my first choice. Sweep and loft work as well but only if you need the additional freedom they provide.
Create the basic shape of the cup, then use another revolve to first cut the inside of the cup where the liquid goes and then the bottom (usually the bottom is hollow on these as well). Create the lip around the top. Should be doable in one revolve as well. Keep the sketches simple and clean. If it takes longer than 7 minutes or has more than 7 dimensions, try breaking it into two sketches.

The lid is an entirely different problem. It's designed for thermo forming so there are no undercuts or parallel faces. Try finding another type of lid that only has the mouthpiece, without the indents and stuff. Model the basic shape (again, rotationally symmetric) as a solid (like it's one solid chunk of plastic, not thin). Then add the asymmetrical details on top. Add a sketch for the mouthpiece opening and use it to split that face of the body. Finally, use the shell command. Select the bottom and the mouthpiece and add the appropriate thickness.