I think there are benefits in learning at a full swing airport, especially procedure wise.
On the other hand learning from a short field will expand the number of aerodromes you will visit including farm strips if you like.
After Norwich (I learned on a PA38 and PA28) I started renting from Modern Air at Fowlmere EGMA , which is a grass relatively short strip (700m). Later I flew Seneca from there.
So both types of aerodromes have their benefits