Yep, it sounds like your water pump is leaking through its seal which lets coolant drip out of the weep hole.
I would only go for an OE quality water pump. The so-called "lifetime" warranty store brand water pumps sold by Autozone, Kragen, etc. are cheapily made and will fail again well before an OE-quantity pump will. Their lifetime warranty is just a low-cost marketing gimmick since they realize few people own their vehicles long enough to still own it when the cheap pump failed prematurely again. My time is worth more than the cost savings are for a cheap water pump.