I know quite well that the plethora of Protestant denominations means that there are almost no universal traditions. However, there are a number of particular traditions or beliefs that are held by the majority of Protestant denominations. In this sense, then, I'm wondering if there is a general consensus - and what the consensus is - as to who can baptize a new believer. An even better answer would be one that broadly categorizes the denominations that have a particular restriction on who can baptize and the denominations that don't have such a restriction. (Brownie points for an answer with a Wesleyan viewpoint.)
Related: According to the Roman Catholic church, who can baptize?