I guess you can just write top to bottom and then right to left like it was done traditionally if i recall correctly.
About the different fonts: just like in the Roman alphabet there are different ways to write stuff: like a vs ɑ. Often there is also a stylistic version used by printers and software and a handwritten variant. i know some hiragana examples: きさりこ all have different variants. The same probably holds true for some kanji. However, I assume that in most cases there is only 1 correct stroke order with the rare exception of having two. Knowing the stroke order will help you immensely to read kanji as it is common for people to not have the nicest handwriting and then only the stroke order will enable to to decipher it.
TO maybe get common with some different styles of writing kanji, i can recommend you to install this userscript: