i use an almond oil based natural eyemakeupremover. before i use a cottonroundthing (you know what i mean) to takeoff eyeshadow and so on, i use q-tips and the remover to takeoff my eyeliner. i think its best to do that first of all, because then its off and you wont smudge all that stuff with the cottonround around the eyearea.
natural oils work best for me, they even takeoff waterresist mascara, but it doesnt work for everony. some people get irritate eyes, red eyes and so on. I got problems like that from nearly every remover i used before that. the drugstore stuff and so on, just didnt worked for me.
for my face....i use a microfiber-cloth and warm water at first. that takes off gently nearly EVERYTHING.
after that i wash my face with a handcrafted soap (saltsoap or alepposoap..).
then i only use thermalwater by avene as a toner, and sometimes when i feel my skin needs some more moisture i use "caudalie eau de raisin" under my moisturizer.
i am very happy, that i found mild, gently and natural stuff to clean my face. because i really think that aggressive cleansers and so on can damage skin.
hth