欣赏 xin1shang3 — is mainly used with inanimate things.
- 你过来欣赏一下这个场景 Come admire this scenery
赏 specifically refers to observing something likeable. Zdic:
佩服 pei4fu5 — is mainly used with people, as you correctly say, whom you look up to, or more generally whom you appreciate and praise. It can be used as "admire" someone's abilities or skills.
- 你女儿高考成绩很高，我很佩服她 Your daughter high school score was very high, I really admire her
- 佩服佩服 Nice! / Well done! (This is a colloquial usage of the doubled verb, used like an exclamation or interjection, closing a sentence.)
- 我很佩服她的努力 I really admire her dedication
- 我很佩服你这么慷慨 I really admire your generosity
赞赏 zan4shang3 — is more used as a noun: "appreciation"
- 为了表示我对他的赞赏，我给他买了一件礼物 I bought him a present in order to show my appreciation towards him
- 谁还不能赞赏圣雄甘地的教导 Who wouldn't appreciate Gandhi's teachings