I would say there were a few main influences to non-Jewish Christianity (over and above Jewish Christianity, which was mainly believing that the Messiah had already came, but still adhering to the Law of Moses etc.).
I wrote it in a nice graph, but I can't do that here...
1. General interest in monotheism in the Middle East/Mediterranean area at that time, and their abandonment of Paganism (though they still refused all the "hard laws" of Judaism- Islam did not yet exist and Judaism was much more numerous and influential back then).
2. General Pagan traditions and already established religious institutions, practices and modes of worship (not to mention European Christianity, and it's traditions and stigmas, which are all Pagan European ( which is the only way they know how to represent any religion).
3. "עשרה הרוגי מלכות" and "כפרת עוונות"; i.e. the idea that the suffering of one person can atone for many (at it's core a Jewish idea, but taken to it's far extreme by Christians).
4. Hillel and peace loving. He lived in the time of Jesus, and was the known founder of the concept of emphasising those ideas (Christians use those kinds of ideas to downplay the law (as do many Jews; Tikun Olam).
5. Philo of Alexandria created a written philosophy for the מצוות not being meant to actually do in all generations.
6. The Essenes group (איסיים) tried to be 'super holy', and for example, many of them didn't marry (they lived at the time).
To me these are the main (mostly Jewish) ideas that went into Paul's founding of "non-Jewish Christianity" in the Mediterranean basin.