Congratulations for what seems to be a level-headed response to your genital warts, and for your desire to protect your partner. You sound like a responsible guy.
You ask almost all the common questions that people have about genital warts, and they have been repeatedly addressed on this forum. In addition to the comments below, you can get lots more information by using the MedHelp search link, and also by reading some reliable web sites about HPV and genital warts. Some examples are the American Social Health Association (www.ashastd.org), CDC (www.cdc.gov/std), and my former employer's information (www.metrokc.gov/health/apu/std), which I largely wrote myself.
Some general points: Nobody should lose a lot of sleep about catching or transmitting HPV. It happens to just about all sexually active people somewhere along the line. Genital warts are an inconvenience, as you have found, but rarely a serious health problem. Still, I agree it is reasonable to avoid exposing a new partner to an overt wart virus infection if it can be avoided.
It is generally believed that the infectiousness of warts is reduced when the warts themselves are gone. However, I stress reduced, not eliminated. Some potential for transmission probably exists. There are no data to say whether the reduction is "dramatic" or only modest. However, even without treatment, most genital HPV infections--especially those due to HPV 6 and 11, the "low risk" types that cause warts--clear up on their own over several months. My personal advice to patients has always been that they are unlikely to transmit once 6 months had gone by after the warts are gone, assuming no recurrence of warts in the meantime. But this isn't hard and fast, and there is no way to predict with certainty.
As your provider told you, consistent condom use will reduce the risk. However, condoms aren't perfect, since the virus might be infecting penile skin above the condom line. The thickness of condoms is irrelevant; the virus doesn't pass through latex.
The final preventive point is that your prospective partner should see her provider about getting the HPV vaccine (Gardasil), which will immunize her against the HPV types that cause warts (HPV 6 and 11), as well as the two most common high-risk HPV types that can lead to cervical cancer. Every sexually active woman should be vaccinated, and you have a particular reason in this situation. However, the vaccine requires 3 doses over 6 months before protection is complete (although there may be substantial partial protection a few weeks after the second dose, i.e. in 2-3 months).
You are correct in your instinct to discuss it with your partner. Don't get the idea you are in some weird minority: the current estimate is that somewhere around 10% of all sexually active people get genital warts at one time or another. Whatever else you decide about condoms and advising your partner about the vaccine, once you become sexually active together she should be on the lookout for warts.
Good luck-- HHH, MD
Before others jump on a minor inaccuracy in my reply: All younger women should be immunized against HPV, not necessarily all sexually active women. The vaccine is approved for use (and usually will be covered by health insurance) in girls and women age 9 to 26. There certainly is benefit for many women over age 26, but it declines with the rising likelihood that a woman has already been infected with the HPV types covered by the vaccine.
Most important, all young women should be immunized before they become sexually active. Gardasil should be considered automatic for all girls before first sex, e.g. before age 15.
Thank you doctor for your reply and comments. My level-headedness is a product of time getting used to it and also researching the area, but it has taken a few months to get here!
Thanks again for your very helpful reply.