Know that the thinnest string is considered the 1st string and the top the 6th. This is often the hardest part to remember. But the bottom string is the first string, not the top one. The bottom string is always the thinnest. Again, this might not feel intuitive, but it is easy to get used to. The bottom string the 1st string -- and it is an E.
You can learn the strings up or down -- but you need to remember which string is which number to help read guitar tabs and talk about notes.
"Heavy" strings are thicker, often wound with a different type of metal, while lighter strings are thinner.