All three of the phrases are similar in that they are about conveying how something, or someone, appears to you. However, they do have different meanings that change the nature of what that appearance is.
"She seems like the type who forgets important things." This is emphasizing how she appears to you, so it may or may not be the case that she does in fact forget important things, but it seems that way to you. You might want to compare and contrast
"She tends to forget important things." In this case you are more certain of your personal assessment, but within that assessment you are saying that while she usually forgets important things, you also allow that she doesn't always.
This would be "she forgets important things easily." Where
~がち is about how often she forgets,
~やすい is about how reliably she forgets. However, as mentioned in the comments, I'm not sure
~やすい can be applied to people. Someone can correct me on this, but I think it would be more grammatical to say something like
彼女にとって、大事なことが忘れやすい, which would be "For her, important things are easy to forget."