I've played against a really good Yoshi with Marth and my Marth is above average. I would say that Marth has a slight advantage against a Yoshi of the same skill level; however, the Marth main has to be aware of Yoshi invunerable frames from his fsmash, his DJC aerials into between your combos, set knockdown from his dtilt and his good edgeguard game on Marth.
Marth has to build up damage in order to begin effective combos usually started from grabs and fairs. It's also possible to gimp Yoshi in between his DJC aerials and perform combo that are incredibly hard for Yoshi to escape. For instance, some Yoshi's like to Full a Bair and sneak in a Nair to add more pressure. You can sneak in a few fairs in between the Nair and start some juggles. A Fair -> weak hit Up air -> Nair (more knockback)/Fair(more combo options) are good starters. You may be able to end the weak hit Up Air with a Fsmash. If he's towards the edge, he's in big tourney and have few options to recover because you got rid of his second jump in between his Nair.
As mentioned earlier, Yoshi's edgeguard game against Marth is actually really good. He can set up a dtilt near the edge which has a set knockback no matter what percent you've accumulated and can DJ edgehog. It's really fast and you are left with low options in recovering back on stage. Good Yoshi's will position you will eggs if you are delaying your recovery and will smack you back off via dtilt, dsmash or fsmash (has leanback and usually performed if you try to fair them in between over B recovery).
Yoshi's combo ability on Marth is great too. Especially when he's directly below you. He'll string together a lot Up Air and will use eggs to rack up damage, continue juggles and make you whiff aerials.
Also note that Yoshi can not jump out of his shield which means that he wont be able to wavedash out of shield to punish missed fsmashes. So it's possible to Fsmash and tip his shield to cause a lot of shield stun to keep him on the defensive. Yoshi can DJC through some of your fsmash into an aerial, so be prudent about how you land the Fsmash.
As far as stage choices go, I think that Battlefield is one of the best against Yoshi because platform will help you with juggles and Yoshi will have a hard time manuevering around your aerials and landing his own. Because it's Battlefield, the Yoshi main will have more trepidation in DJ edgehogging and that will reduce his edgeguard options. PS and FD are great for Yoshi and on average you wont be killing Yoshi until really high percents (110-130%) with most of your kills being from up tilts, fairs combo into tippers, Ken combos and reverse Dolphin slash. This matchup definitely should not be overlooked. You will need to know how to play this matchup or you will get owned!