I'm a mario main. pretty experienced so i think i can be of some help.
For mario's approach, i find it effective to short hop fireballs while running in, and sex kick into downsmash if the last one i fire(the one that would hit just as i get close enough) hits. The fireball provides some good stun and an opportunity to get in a quick aerial. fastfall the sex kick(Nair) and go into a downsmash as soon as possible, as this is mario's fastest smash attack. At low percentages, short hopped aerials, except his f-air, are very useful.
As for finishers... Well mario's best finisher is his fsmash, but that can be a bit tricky to sweetspot. All his smashes can KO at high percentages. And dont forget, in brawl his f-air is actually a useable off-edge spike.
Edgegaurding's pretty useful for mario. Basically, you want to go with back-airs. They come out fast with good knockback. The cape is also useful, albeit situational, as it completely turns the oponent around. So, against, say, fox, if you cape his illusion or firefox, he'll turn and be move away from the stage. Mario's front air works as a spike, so if you think you can hit it, go for it. Other than that, edgehogging is also good.
Mario's recovery isnt too hard to do. He lost his tornado for recovery purposes in the melee/brawl switch, but i don't think its so bad really. For mario's recovery, You cape or double jump in any order, then up b to get the ledge if it isnt being hogged. Otherwise shoot high and get directly on the stage. I did have one instance, where i was very far away and had a full charged fludd. I caped AWAY from the stage and fired fludd, which pushed me towards the stage some, and then was able to recover. not sure how practical this is though, i havent tested it much. Other than these things, keep in mind that mario CAN walljump, it's useful, though situational.
Combos... well they're much harder in brawl, but i find grab->Dthrow->Usmash to work pretty well. I also find all of his aerials besides his fair to be useful when trying to combo, particularly the nair and uair. Mario's utilt is a good juggler, and he can decently use the wall of pain.
I hope im not forgetting anything, but besides the above its the same as most characters. Sheildgrab works wonders if you use it right, good spacing is key, and teching is always a good skill to have. If i forgot anything let me know and ill be happy to clear it up.
fireballs are Mario's best approach