[action verb + 起来] does indicate beginning of an action, e.g. 动起来 = start to move; 打起来 = start to fight
[verb + 上] doesn't indicate beginning of an action, it indicates 'action toward an object' e.g. 爱上他 = fall in love with him; 算上他 = counting him; 走上絕路 = walk toward an dead end
[verb + 起来] could mean [upon + verb]. e.g. 看起来 = upon looking (seems); 聽起来 = upon hearing (seems); 说起来 = upon mentioning (by the way)