I’m also a newbie and it’s a work in progress but:
A and U are easy as first and last.
E: i’m righthanded so the “letters” are on my left hand. If you look at your left hand the three middle fingers look like an E on its back, so the index finger is the top of the letter E.
I: the longest middle finger. Also - random fact that reminds me: i used to live in Italy where I was startled to find that certain letters are not used except in foreign words: letters j, k, y, and a few others were not even included in the Italian alphabet. There isn’t a natural sound that means J, they call it “Long I” because it’s like an I with a tail. The same is true in Sign: J is drawing along the middle finger and round to the thumb. So I is like short J!
And as for O, that one’s easy: it’s the finger with my wedding ring on, which is a nice visual mnemonic.
Though if anyone comes up with better ones, please tell! Those are just what I’ve come up with so far.
FWIW I’m also practicing with the Twinklefingers Fingerspelling app which is good for attempting to get my brain up to speed in those idle ten minutes on the bus...