Well, the main point is to satisfy whatever bits of your brain think the matter isn't really settled for you -- that you either might or should re-evaluate some of those claims if exposed to them. (Assuming I'm right in guessing that there are some bits of your brain that think that, and that that's why you feel the way you do.)
So the question is probably what makes sense to you. Maybe you should try to identify one particular Christian claim or argument or piece of alleged evidence, one that triggers those avoidance reactions more than most, give it a good examination, and see (1) what you conclude about it and (2) what effect, if any, this has on your feelings about pro-Christian and anti-Christian arguments generally.
If you do this, you might want to make sure your brain is well informed in advance that coming to a particular conclusion on this point alone doesn't commit you to any particular position overall. (Which it doesn't, unless the rest of the evidence seems very finely balanced to you.) Because otherwise some bits of you might be worrying that other bits of you will be biased in how they look at the issue for fear of reaching the "wrong" conclusion.
If you do this, what to do next probably depends on the outcome -- both in terms of any ensuing adjustments to your beliefs (Christianity more/less probable than before) and in terms of any effects on your feelings (more/less/different "ugh" feelings when you contemplate Christian propaganda).
I've noticed during my thoughts on the issue that I seem to be biased against Christianity- although raised in a Christian household, I have noticed that I become more tense when reading effective arguments for Christianity and more relaxed when reading good arguments against it- I also feel strongly tempted to pull out books which I know give good arguments against Christianity.
I thought the issue of whether Christianity was actually true concluded- but given that I am now aware I'm biased, it's difficult to be sure. On the one hand, there is a lot of evidence against it (biblical contradictions etc...). On the other, there are some pieces of evidence that appear false 'on the surface' but which seem plausible when I take my bias into account.