Probably a popular choice but for Town/Field music it is National Park and Ecruteak/Cianwood City, both the GSC and HGSS versions. Despite only being allowed an hour of gaming time in my early childhood I would still return to both places in GSC just to listen to the music. It is soothing in a very special way, even today. Reminds me of simpler times...
Battle themes are a tough choice... of the top of my head I'd say Giratina and Colress. Both feel super unique and out there, without sacrifing catchiness. And considering you usually only hear them once per playthrough, they make a very good impression.
I should listen to the soundtracks again, there are so many good tracks to talk about...