Welcome to the forum and thanks for your question. I'll try to help. However, questions about risk of exposure, or of infection if exposed, and about the potential future health problems of a particular STD -- which is the case here -- are always more or less identical. If you have reviewed other HPV related questions on this forum, most likely you can predict my response.
Believe it or not, your new partnership, and your partner's current or past HPV infection, make little or no difference in your risk of catching HPV, either genitally or orally, or in the chance you'll ever have an HPV-related health problem.
Your comments don't make it clear whether or not your partner still has a positive test for HPV, or of cellular changes caused by HPV (detected by pap smear), or neither of these. Since HPV DNA may persist forever in all infected patients, that may be all her doctor means by telling her that "DNA remains". Anyway, persistent DNA does not in itself mean HPV can still be transmitted. Usually it cannot, once the cellular changes (the abnormal pap smear) have cleared up -- which is probably what your partner and her doctor means by "beautiful" results. So I am inclined to doubt your partner's (past?) HPV can still be transmitted to you.
And even if it were, what would it mean? Probably nothing. The vast majority of HPV infections, especially in men, never cause symptoms, do not lead to cancer or anything else, and clear up entirely within months or a couple of years. In other words, even if your partner were known to have an active, transmissible HPV infection at this time, I would advise that there is no need to take any precautions agasint it.
So all things considered, I would not advise you to limit your sexual expression with your partner. All practices should be fair game, including vaginal or anal sex, oral sex (in both directions), or anything else as long as you mutually enjoy it. (Of course this assumes neither of you has any other STDs aside from HPV.) This doesn't guarantee you won't get HPV, because I have no way of knowing for sure about the status of your partner's past infection. And of course she could have other HPV infections in addition to the one detected by pap smear. Most sexually active people have multiple HPV infections over time.
Having said all that, I understand your desire not to acquire HPV if it can be avoided by reasonable precautions; it's just that I don't think avoiding intercourse or oral sex are "reasonable" in this situation. You could use condoms consistently for vaginal or anal sex, which would reduce but not eliminate the risk of transmission. And you could consider HPV vaccination. Although officially approved only for people under 26 years old, it sounds like you have been at lower risk than many men, and might still be susceptible to one or more of the HPV types covered by the vaccine.
The bottom line is that nobody should HPV stand in the way of romance, commitment, and rewarding sex. The risks simply aren't high enough to let an impersonal bit of DNA -- which happened to evolve to exploit human intimacy for its own propagation -- have an important impact on life.
For further reading, here are some past threads that deal further with some of these issues.
http://www.medhelp.org/posts/show/1522088
http://www.medhelp.org/posts/show/1711835
http://www.medhelp.org/posts/show/1222683
I hope this has been helpful. Good luck-- HHH, MD