The opening song, "A Trick of the Tail" is about a beast from another dimension who comes here to explore, but ends up being put in a zoo. "Congo" is another bizarre choice, it's a rock song that is definitely not romantic. A better choice fun that same album, "Calling All Stations", would have been "If That's What You Need", or even "Shipwrecked".
Not all the choices are ridiculous. "In Too Deep" is a true ballad from "Invisible Touch"; "Throwing It All Away" should have been here with it. "Hold On My Heart" is definitely a keeper fit a collection like this. It's from Phil Collins' last studio album with the group, and he is definitely responsible for writing some great romantic ballads, some with Genesis, but mostly in his solo work
"Man On The Corner" is a very beautiful song, not really romantic as it's about a man who basically has nobody in the world, but there is a softer tone so I'll go with it. "Many Too Many" is a similar song, maybe closer to being romantic.
"Looking For Someone" is the oldest track here, maybe the rare Peter Gabriel-era Genesis song that came close to being considered a romantic ballad. It's a very pretty sounding song that would generally fly under the radar of the casual fan.
The point isn't that any of these songs aren't good, there is actually some great great stuff here, but by and large they aren't romantic ballads. Genesis is not generally the group you would put on after lighting a fire and spreading out rose petals. They HAVE made some wonderful romantic ballads, many of which have mind-bogglingly enough been left of this collection. This isn't even a great collection to introduce someone to the band, there are many others on this site that will do a better job of that. Just pick more wisely when trying to impress your loved one. Hopefully I've saved your relationship with this warning!