My two cents:
The present tense is good for high-action, fast-paced stories where the author wants the reader to be running by the MC's side. Objects fell onto the reader as well as on the MC, and situations take place before the reader realises what's going on. Despite how bad it is written, and how weak the story is, IMO, the usage of present tense is one of The Hunger Games key features leading it's success, because of the "immediate" feeling. E.g., Emilio Salgari's Sandokan, another very fast-paced story, should have been written in present tense.
On the side of the cons, first person present tense (as K L van Kriedt is writing) allows little to none second thoughts. "Had I known" is an impossible expression in present tense. Foreshadowing is also impossible. A large set of techniques possible in past tense are impossible in present tense, because the narrator is clueless about what will happen, contrary to writing in past tense where the narrator knows the outcome. The argument that the reader never knows whether the MC will die has no grounds. If the MC die, the story would be abruptly stopped, which would make no sense--that's one of the reasons why The Hunger Games is soooo poorly written IMO. There's no way Katniss would end up dead, so there's no actual suspense there.
Writing in first person present tense is also difficult because the POV needs to be deep. I.e., in past tense, you can write: "I opened the door and wondered if he was hiding there in the kitchen"; in present tense it's almost foolish to write: "I open the door and I wonder if he is hiding here in the kitchen". Of course, you can put it that way if you like, but it sounds almost idiotic. Because the action is taking place RIGHT NOW, the thoughts have to pop-up immediately: "I open the kitchen's door. Is he hiding in here?" You don't write a thought in italics when you're writing in first person present tense, because you place the narrator's thoughts within the prose itself (like in the previous example), otherwise the feeling of "immediate" is broken. Mastering this way of writing is kinda tricky, but it can certainly be done.
Past tense allows forbidden techniques and expressions in present tense (foreshadowing, "had I known", "now I regret the decision I made back then", "the surprised that followed..." etc) to be used. Also, it allows greater introspection and it's not that tricky to write--all of us have read tonnes of stories in past tense, so we're more used to it. I disagree with those who state first-person present tense brings the MC closer to the reader. A close relationship can be easily achieved using past tense.
Finally, K L, I would like to point to the fact that your story takes place back in the 1960's. At least for me, it's difficult to think of your story as happening right now. Many YA stories are written in present tense nowadays, but, also, they are supposed to take place by the time the reader reads the story, either if the reader reads it in August 2016 or in May 2017. The Hunger Games takes place in an unknown future. The usage of the present tense makes that unknown future more real and allows a greater suspension of disbelief. I'm sure about a story taking place in the past (1960's).
In the end it's your decision. I'm not a pro writer, of course, so take my advice as limited as it is: I would write your story in first person past tense if I were you.
Kiss,
Gacela