The easy way to know whether it’s ‘I’ or ‘me’ is to remove the other half of what you’re saying, so
(Billy and) I went to the park.
She came to the park with (Billy and) me.
Myself is reflexive, which means that you use it, broadly, when you are ‘doing’ something to yourself:
I washed myself.
I woke myself up.
I looked at myself in the mirror.
‘Myself’ is not a synonym for ‘me’ though.
‘Me’ and ‘I’ can be a bit complicated by the fact that we now say ‘me’ at times when we used to say ‘I’ but it’s accepted as common usage, eg people used to say ‘it is I’ when they now say ‘it is me’ - think of ‘Allo ‘Allo with ‘it is I, Leclerc’. But mixing those up doesn’t bother very many people nowadays.