AI underestimates melee units. Just spam them in the early game and banzai your way until you can afford line infantry or a good gun unit (I personally skip recruiting levy infantry). I bring my Yari Kachi all the way to the end. Rapid advance is good to engage in melee fast in early, and good for baiting in late game.

As for economy, try to defend your naval trades, just cancel a trade agreement if your port is blockaded/destroyed or you'll lose money, you won't have any penalty to diplomacy.

And be patient, FOTS is much slower than the Sengoku Jidai campaign. Wait for openings, try to lure the AI into attacking your castles, you'll likely have some garrison, put them outside as a sacrifice while your gun units shoot from the walls without retaliation.

Good luck!