Genital warts are caused by HPV. There is no cure for HPV. Sometimes, after years of having HPV, the body just seems to fight it off one day, but you shouldn't necessarily count on that happening either.
You can have the warts removed, but you will still have HPV. You will still be able to give HPV to any partners you have, and you still may break out in warts in the future.
I have never had LEEP, but I think it might hurt a bit. I have heard that people may take one to three days before they can resume most daily activities, but they may have to wait one to three weeks before having sex again.
As far as having futures partners, I would suggest always using a condom. Condoms reduce the chances of passing on HPV, but they certainly do not eliminate it. So you should always tell potential partners about your HPV before doing anything sexual with them.
If a guy has a problem with it, let him go. Warts aren't uncommon, so you might even be able to find a partner who also has them! There are even dating sites for people with various STDs so that they have a place to meet people, be up front and honest about their STD, and not have to worry about infecting anyone else.
Did Planned Parenthood say that they would help you get LEEP or anything else?