Alright, I'll work on ordering the anime songs atm, then start on classic.
Well, I have a list in order of arcade, up to date, (Translated) Looks like anime really sparked in Arcade 9. Also, all info is from wikihouse. No0t every song, but all I could dig up.
SPOILERTaiko no Tatsujin Anime Song, Order by Arcade.
Arcade 1: None
Arcade 2: Song of Gatchaman, Chan counting rhymes, Doraemon Ondo, Family Sazae-san, Anpanman march.
Arcade 3: A Cruel Angel's Thesis
Arcade 4: Mystical Adventure!, Love song of the Lamb, Doraemon no Uta
Arcade 5: None
Arcade 6: None
Arcade 7: Chu in Hamtaro - Tokouta take Norinori -- GALAXY EXPRESS 999 Arara spell
Arcade 8: Happy ☆ Material, Namikaze Satellite, Hamtaro take Tokouta 2005
Arcade 9: Spurt!, TONIGHT×3, Re:member, Kur ♥ carp, Halle Reyukai Clear, In Yuruyuru DE-O!, Love it, GoGo Sentai Boukenger
Arcade 10: Motteke! Sailor Fuku, Climax Jump, Silver sky, Happy ☆ 彡, Gegege no Kitaro, Allegro Cantabile, Together, Anpanman gymnastics
Arcade 11: DIVE TO WORLD, DAYBREAK'S BELL, distance, After Dark, Jungle P, Genesis of Aquarion, Precure 5, Full Throttle GO GO!, Chance!, Pururun! Shizuku-Chan, Doraemon is a dream come true, Engine Sentai Go-onger, Bottom Biting Bug, Also link hands and hearts get connected! !
亜 <--- I Think this is the asian release? None on here anyways though.
Arcade 12/12.5: Tank!, A Cruel Angel's Thesis (music desk back), 88, Kirara Kira Kira ☆ 彡, Turbulent, Triangler, CHU-BURA, ( RISE? Wikihouse not sure I guess? ), Cloudy, Over the Future, Yugoshugo you!, Anataboshi, Bluebird, Courage 100%, Song Yatterman, Kinnikuman Go Fight!, High Touch!, Samurai Sentai, Journey through the Decade, Dragon Soul, Let's! Fresh Pretty Cure!, Which Dora Doraemon Ondo odore
亜2: Hello Darwin! - Demand curiosity ~
Arcade 13: Tank! (Music desk back)