"I don't think I'd better" is a nonstandard/rregional way to say "I don't think I should." I would recommend not using it, unless you are trying to master regional dialects. "I don't think I should" is a safer choice. "So you want to go hiking?" "I don't think I'd better/ I don't think I should. My broken leg is still healing, and I might injure it again if I start hiking again too soon." "Should I use this regional structure when I speak?" "I don't think you should. Standard structures are usually safer."

I usually use this in the positive. I'd better go. In this way, it's like "I should".