The difference between present perfect "-te iru" and past "-ta" is that the result of "-te iru" is still valid at the current point in time, while "-ta" is not necessarily so. For example:
okite iru: "has woken up" (and is still awake right now). The emphasis is on the current state of being awake, rather than the past act of waking up.
okita: "woke up some time in the past" (but might be sleeping again at this point)
Or a very classic example: kekkon shite iru, "is married" (not "is currently marrying").
One important exception (that I only learned recently myself) is subclauses modifying nouns. Take the words hankachi-fu (handkerchief) and kawaku (to dry). If you write: hankachi-fu ga kawaita, it means that the handkerchief dried at some point in the past (but maybe soemone dropped it in a puddle since then). However, if you write: kawaita hankachi-fu, this should be interpreted as kawaite iru hankachi-fu, that is, a handkerchief that is currently dry. This is not always the case though; sometimes the past -ta form is really meant.
Finally, if you want to make your sentences shorter and more informal, just drop the "watashi ha". Most times it's redundant because it's clear that you're talking about yourself.