Vaseline right from your medicine cabinet will do the trick.
I also use Mary Kay Eye Make-Up remover. It is especially good for removing mascara.
...and get an extra tube of lipstick.
Did you know???? When you get to the top of the lipstick where metal meets your lips, there is another tube waiting for you below? Many years ago I ran my favorite lipstick down to the metal. Not only that but it was discontinued. I was not happy until I remembered my lip brush...that was years before lip brushes were standard equipment in a make-up drawer.
If you don't use yours or even have one, pull it out or buy one. You will have some more of your favorite lipstick! And, best all all save some money.
When putting on eye make-up, always use your ring finger. I read this in a magazine sometime, somewhere.
It seems the ring finger has the least amount of strength, even less than your little "pinkie".
When working around you eyes, you don't want to apply too much pressure and break down the tissue/muscles? I started using this tip after reading the article. It didn't take long to make it a habit.

I cannot honestly tell you if this is helping the tissue around my eyes stay firm...I am not taking any chances! Now to find out what to do about the circles :)