how do i know if a move is correct?

Well, e4 is more typical, and while it's good to castle it's not usually necessary to rush it. If you want to castle on the kingside, You'll probably want to make both those moves during your opening (others are available, but those are extremely common). e4 is useful because it immediately puts a piece in the center in a way that your opponent must respond to in some way, and it also prepares the bishop for development, so it's a multipurpose move. Nf3 is a common followup depending on how black responds, because it defends the pawn on e4.
By playing the other way around, you're not going to castle any faster, and you might give your opponent an opportunity to prevent you from playing e4 with something like ...d5, which isn't the worst for you because you can still play e3 and get the bishop out, but I'd question what you're achieving by letting black grab all that space early on.

Improving Your Chess - Resources for Beginners and Beyond…

https://www.chess.com/blog/RussBell/improving-your-chess-resources-for-beginners-and-beyond

ok, thank you for the tip