Well on the ground, you should be shooting fireballs. A short hop can fit two fireballs, while you DI forward or backward towards/away from the enemy. When you see your chance to hit, you quickly short hop into an aerial, and as said by Faith, fast fall afterwards to minimize risk. If you space your attacks properly, they are actually quite safe to use (especially bair). Know your enemy though, its a lot harder to hit Marth and characters with long (and like Marth, disjointed) hitboxes. In those kind of situations, you short hop and DI your first aerial away from your enemy while they attack, then quickly come back with a second aerial off the short hop, or land and do another short hopped attack if you have the time (usually you don't).
A shorthopped fireball into a tornado is a good move early on if the fireball connects. It gives you just enough time to quickly swoop in and hit your enemy with the tornado. From there, you can either "chase" the enemy and rack up hits, or "sweep" through the enemy and space yourself away from their attacks so you won't get punished for your ending lag. Tornado is useful, as long as you use it wisely, otherwise you will get punished.
Another move you can use to a lesser extent is the Dash attack. While most people disagree about using it, as its easily punished, there are some situations where its useful. With proper timing, you can do a "pseudo" lock on your enemy with the Dash Attack. Imagine Final Destination: your enemy is landing from a missed aerial and is about an inch and a half away from the edge. You initiate the Dash attack before your opponent actually hits the ground. Chances are, if your enemy doesn't expect it, he/she will not have the time to DI (I don't think you can Smash DI out of it at all), and will be hit off stage by the knockback of the last punch. In a perfect world, you can't proceed to edgeguarding them, but the situation doesn't always play out that way. If you use the move too much, people will get wise to you, and punish you.