Peaches Castle - It doesn't matter which remake you enter first but you are given a prop in the second remake and a random item in the first. Even if you don't get a prop in the first remake, getting a item that's right of the prop on the item menu will be faster than getting one to the left (because if its on the left you have to press right to use the prop)
8-1 - Use the prop on this level to enter the pipe early. Try not to lose the prop since the last 2 star coins are faster with prop
8-2 - Get the fire flower to help kill the enemies that are in your way, you need to be big to get the last 2 star coins
8-3 - Continue using the fire flower (the second coin needs it if you don't want to damage boost)
8-7 - Grab the Prop from the red coin ring
8-T - Use the prop (The second star coin can be inaccessible if the p-switch timer runs out)
8-4 to 9-C - Try not to lose the prop, you can get the rest of the star coins without it but 8-5, 8-A, and 8-C become easy with them