I want a new iphone, but I don't want to lose my message threads

I am considering purchasing a new iphone (I currently have the iphone 5s and I have it with Straight Talk) but the thing is, I'm not planning on keeping the current iphone, which has about 8, 9, 10 maybe message threads from my friends, family, boyfriend, etc that I want to be able to transfer to the new phone. These threads start way back, like 10+ months ago. Is there any way of possibly getting these threads to show up on my new phone? Because if not, then I most certainly am not getting it.

I also really want to make a new apple id, so if there is a way of doing it that is not through icloud, that would be even better. but if it HAS to be this way, then so be it! I just want my messages, that's more important than a new apple id!