A Mr. tails the fox suggested that I instead do a thread per world rather than stage, so I came up with a system where I constantly edit in new stages to this one post. It'll have to be a matter of patience for you guys. Also, I realized that this is probably the least useful of the Game Guides on here, but I guess you can have a laptop next to you while playing.
Okay, on to the stages!
World 1-3
Star Coin #1
This is impossible to miss, as long as you have a Yoshi, which are introduced in this stage. Just follow the trail of small coins using Yoshi's flutter jump (press and hold the 2 button) and you'll fly right into it. A Propeller Suit will also work.
Star Coin #2
Later on, you'll see a group of three green pipes with Piranha Plants next to each other and then a yellow and green pipe on a ledge right after. Jump down onto the right pipe of the three green ones (Yoshi is immune to the Piranha Plant's teeth) and walk into the ledge to find that the yellow pipe is split in half. Go down the lower part of it to grab the Star Coin underground with Yoshi or a Propeller Suit.
Star Coin #3
It's high above an L-shaped red pipe with a 'Plant in it. Get it the same way you got the others, with Yoshi or a Propeller, jumping from the top of the red pipe.
Secret Exit to World 1 Warp Cannon
This is the only secret exit in World One, and well worth the honor. To find it, jump on the ledge that leads to a hidden room right before the third Star Coin. From here, try flutter jumping with Yoshi or using a Propeller against the wall above the room entrance and you'll land on a ledge hidden from view. Walk right and you'll come into a pipe. On the other side is the secret flagpole, marked by being red and black. The Warp Cannon it leads to takes you through half the game, plunking you in World 5.
World 1-Fortress
Star Coin #1
It is clearly visible on the left side of a swinging platform. Jump on the retracting platform to reach it. Timing is vital!
Star Coin #2
Above the first coin, there are 3 swinging platforms. The path seems to say go up left, but if you wall jump up the right wall, you will find a hidden area with the star coin.
Star Coin #3
In plain view above the shuffling item block. Wall jump up the shaft beneath to get it.
Boss: Larry Koopa
This guy has two attacks: a magic shot and a shell dash. The magic can be cancelled out by an ice flower shot. Larry will start by shooting magic, and then jumping across the platform. When you get a chance, jump on him or throw fireballs at him. One stomp or 6 fireballs will cont as one "hit". Once hit, Larry will get in his shell and go back and forth and then pop back out. Repeat this method 3 times and he's done.