While I love a new playthrough and a fresh new start. I'd say the start of my run is probably my least favourite, mainly because it's really slow and I'm always waiting to get to that one point in pre-hard mode where things start to kick up speed. Setting everything up and having to wait on some occasions is what turns me off of a run most of the time.
Pre-Plantera though is where I feel the game is at it's best. And that's because it's the exact opposite of what I said above, you finally have your footing and can take the game at any pace you want.