So... There isn't much of a debate within the historical community; authors like Carrier and Price are generally not taken seriously as historians. Applying to the works in the NT alone the usual methods of genre analysis, source criticism, textual and contextual analysis, that are in one way or another used for all ancient or medieval works (which are frequently fantastical and composed hundreds of years after the events) it is simply very hard to arrive at any conclusion other than Jesus existing at least in a minimal sense - as a Jewish preacher baptised by John the Baptist, with a following known as "the twelve", who probably spoke in parables and said "Amen, amen..." (literally Indeed, indeed, usually rendered Truly I say this to you, etc) a lot, and who was executed by Pontius Pilate.

Those who argue against the existence of Jesus do so by appealing to their audiences' unfamiliarity with ancient sources, posing unreasonable demands like "documentary evidence", "eyewitness accounts", "contemporary sources", often with highly mobile goalposts, or the all-too-frequent "show me a character whose source situation is exactly like that of Jesus, whom I in my ignorance am nevertheless familiar with (no list of obscure Roman consuls!) and am ready to admit the existence of". It's a pointless debate to engage in - if you try to illustrate the scarcity of sources by examining a figure like Alexander the Great (since that level of fame is usually required for the average person arguing against Jesus' existence to be familiar with them) it will be twisted into "oh, you're trying to say Jesus is as likely to exist as Alexander?".

All that in mind, I suggest Ehrman's "Did Jesus Exist?" for starters ("How Jesus Became God" is great as well, it's a good followup read). The book is written in a bit of a hyperpedagogical manner, but it straightforwardly presents the evidence and examines the unreasonableness of mythicism. Honestly, don't bother with Carrier or Price, their works simply aren't good history. OTOH, Ehrman's entire bibliography is a goldmine.