About how long will it take me to get to the 15th prestige?

Not sure how long it will take to prestige, because I don't prestige but sam turrets get you lots of xp, using hardline will get you killstreaks 1 kill earlier which will help a lot. Hardline pro also lets you change contents of care package, so if you get lame ammo, you can swap it and maybe get a chopper gunner or sam turret. Also, play headquarters, lots of xp.