Attention Baseball Fans!

I've never been to Houston and want to visit next summer to watch a baseball game. 1) How far in advance should hotels be booked? 2) Which hotel is best to stay at with a budget of max $200/night, that is safe and near the baseball field? 3) Do they have shuttles for before and after the game or is it best to Uber back to the hotel? 4) What else should I know?