As others have said, once you are in love with the girl, you won't feel the need for the magazines. So when a girl comes round to your place first of all, hide the magazines in a locked wardrobe - if she stays the night, say you left the key somewhere else... If the romance looks serious, then as others have said, you won't need the magazines, and can recycle them...
Girls have similar desires to men, but they feel physically attracted to men in different ways. They will notice when you are out together that you look at girls, and equally they will flirt with men. So as a loving and understanding man, you will accept that your girl will flirt, but also if you do the same with another girl, be prepared to "back off" if your girl disapproves.
Single men need to satisfy themselves physically because of prostate cancer. It's the most common form of cancer in men, and the third most common form of cancer in western society. It is important that the system is flushed out regularly, to reduce prostate cancer risk, either by yourself or as part of a loving relationship with a partner.
One guy I know hid his magazines in the boot of his car... then one day the police stopped cars for a routine check and searched his car.... so go with the locked wardrobe idea...