The 7.3fx is exactly what you describe you need: a hybrid road/trail bike that leans more towards roads.
As Sixtyfiver said: get some CX tyres and you'll be fine.
I use the Schwalbe CX comp's and like them very much ... they are light, cheap & versatile
It may not be exactly "the best" ... but I find it to be the perfect equilibrium between weight, puncture resistance, speed on roads, grip on mud and price.
I bought mine for about 8€, which is well below any other tyre in their range around here.
A few days ago I heard a clicking sound on my back wheel ... it turned out to be a small pointy stake of springy metal that had entered the outer wall of my tyre, hit the puncture resistant layer and was bended back out a few millimeters further.
Back home I could easily remove it from the tyre, which was still in perfect condition, apart from a tiny little hole.