I just got my Blackberry 9700 - but it seems that after a day or so, my text messages disappear. Can my phone be set so that the message stay for a set period of time or forever, unless I choose to delete them?

By default 9700 has "bubble" message display. If you receive / send new message with the same contact it'll display only last message, if you click on it - displays full conversation.

To change messages removal on phone open messaging -> BB key -> Options -> General options -> Keep messages (on bottom).