Always, always, ALWAYS check the traveling cart on Fridays and Sundays. There is at least one thing you must buy from them in year one if it shows up as available and you're trying to complete the Community Center before Summer Year 2: Red Cabbage (either the crop itself or the seed). Red Cabbage seeds are only sold in Summer Year 2, so it's basically the main bottle neck if you're looking to complete the Community Center in Year 1. Other stuff that would be nice to buy (but aren't strictly required) are a Duck Feather, a Truffle (Chef Bundle), and maybe wool and/or cloth unless you get lucky with Emily and receive wool as a gift, or get the cloth from recycling newspaper.
One word of advice for min/maxing purposes though: Don't complete the Bulletin Board section of the Community Center until at least Spring Year 2, Day 1. Why? Because Kent comes into the game on the first day of spring in Year 2, and if you complete the Bulletin Board section after he introduces himself, you gain 2 hearts of friendship with him like you do with all the other non-marriage candidates in town. Speaking of Kent, you might also buy Roasted Hazelnuts or Fiddlehead Risotto if it shows up in year one since Kent's birthday is in the first week of Spring. You can easily gain 4 to 5 hearts with him in your first week depending on how you play it.