I was told that you should never just tell a story in your monologue, that the kind where you had to show reaction (like where there is a "(beat)") are the best. I really like my current monologue, but it doesn't have any reaction lines.
Should you only pick from those kinds of monologues?

Do monologues that show off your ability. People like reaction monologues because it shows how you react, but story telling can be great. However, it depends on what you are auditioning for. SO! You should have more than one.

I also heard, you don't want the kind that deals w/"time",ie "I remember..."

Most acting teachers I've ever worked with say to stay away from "story" or "memory" monologues, but there are a few cases when they can be useful. That's only, however, if the character has a very specific reason for telling the story to another character, because after all, the whole point is to get what you want from someone else, right?

For some reason, one that leaps to mind is from Company, if you're familiar with the show. It's a scene where April has come home with Bobby (the main character), and Bobby tells her a story about a failed date he had once. If an actor used this monologue for an audition and just stood up there and told the story, chances are the monologue would fall flat on its face. But in the context of the show, the whole purpose of the story is the very real and actable objective of trying to get April in the sack, so an actor auditioning with the monologue could use that to influence the environment he creates, bring out the subtext in the words, etc.

Anyway, there's my two cents. Sorry if you aren't familiar with the show, but that's the example that leaps to mind. Break a leg with all your auditions!

Thank you for replying. I probably need to change my monologue then, it sounded good at first but looking at it judgmentally it really does sort of lag, I guess I see the importance of an "interactive" sort of monologue.

Thanks for your opinions!