chain grabbing works wonderfully against space animals. There should be a guide to getting around falcos lasers in this forum somewhere. Also to elaborate on bluedeath's comment you should be countering lasers when you predict an approach from falco right after, so what will happen is youll counter the falcos laser and smack the falco as he comes in to kick you, this is really useful against an aggressive falco who always follows up his shl with an attack, eventually your opponent will wisen up and start being more defensive, but anytime you notice a player being overly aggressive (like following the same attack pattern) you should do this.
Marth is the master of gimping space animals recoveries. If you predict a phantasm you can use marth's "jab" (a button once) to either protect yourself or to sometimes smack them out of it. if you are close enough to the edge any time one of the space animals is forced to go into a firefox it becomes an almost guaranteed kill for marth, don't be afraid to jump out and whack them out of it, or if they aim it at you use counter, marth absolutely destroys the recoveries of the space animals (for examples of how to properly edgeguard fox or falco watch mew2king's or kens marth, they both edgeguard really well, and aggressively).
Although this is general advice: space, space, SPACE! Try and keep your opponent at the edge of your sword always, also space with grabs... marth has the longest grab (not counting samus and the links) in the game and most begininning marths are so focused on f smashing their opponents into oblivion that they forget his amazing grab game.
Go to the top of the marth forum and look at the video database and study what pro marths do against fox and falcos, who better to learn from then the best players themselves?