Surely, as a Christian, the New Testament is "the Bible" for you, and you can either accept everything written in it or not accept everything written in it, which is surely "picking and choosing".

Denied. The dichotomy is between "accepting everything in it" and "not accepting everything in it." The latter is NOT the same thing as "picking and choosing."

"Picking and choosing" implies random or personal opinion-based selection. There are other methods of selection. And everyone uses some method of selection. It is a collection of religious texts, not a dictionary.

You are looking at the Bible like a teenage fundamentalist evangelical. Indeed that is exactly the argument that I have heard such people use -- "you either have to accept the whole thing" (by which they mean accept THEIR interpretation of it), "or you're just picking and choosing."

But it is a thing that requires interpretation. Like I said, it's a collection of religious texts. It's mythos not logos. Taken "literally" it leads to a dead end alley of contradictions and red herrings. NOBODY takes it literally. Really. Nobody. They may SAY they do, but they don't, and usually you can defuse their claims by a few well-chosen examples (these vary depending on whom you're talking to, but since usually it's fundie evangelical protestants, there are a few juicy verses from John 5 and 6 that they most emphatically do NOT take literally).

One thing about Christian belief which has always puzzled me is the fact that Jesus was the long awaited Messiah who would come and save his people ( i.e. the jews) but when he did come he was rejected by the very people he was sent to save! Now what was the point of that exercise? Was it a case of, if plan A doesn't work we'll move to plan B ( i.e save non-jews)? It all sounds very messy and ill thought out to me.

This is a common misconception (no pun intended). Jesus was not rejected by "the Jews". He was rejected by SOME (indeed arguably MOST) of the then-living Jews. But not by "the Jews" which without qualification means "all Jews". Some Jews accepted him. Quite a few, in fact. Buncha fishermen, for starters. Christianity was for some years considered a sect of Judaism. There's a reason for that. If I recall, the Christians were ejected from the synagogues shortly after 70 CE, and the two groups went separate ways. But before that Christianity was another sect of Judaism, not too unlike the Essenes in that sense.

But really after the destruction of the temple (70 CE), Judaism became quite a different religion. It moved from being centered around a system of ritual slaughter, to being centered on a constellation of family meals and prayers. It is not too historically weird to say that Rabbinic Judaism and Christianity are twin sons of Temple Judaism. And unfortunately their sibling rivalry has had some very terrible consequences down through the years. Hopefully they're finally learning to get along with one another in the last 60 years.