Your first question
Settings > Application Settings > Default Messaging Application
As far as making certain texts private, I think you have to make an online handcent account, then you can add individuals to your privacy box. But I'm not 100% sure on that. Someone else might know, though.
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1) Turn off all notifications in your stock SMS app, and your SMS/MMS messages won't trigger the stock app anymore.
2) It's been a while since I used Handcent (I use GO SMS myself), but if I recall correctly, Longpress on a person in the conversation list and you should have an option to make it private.