I encountered this sentence in a textbook
野菜をたくさん買ったので、店の人に家まで届けてもらいました。
Which one of the following would the sentence is supposed to mean?
Since [I] bought a lot of vegetables, [I] had a guy at the shop deliver the vegetables home for me.
or
Since [I] bought a lot of vegetables, I received home delivery.
Does the verb もらう in the form ～てもらう always mean to have someone do something for me instead of only to receive something?
The second reading is not valid. When a もらう is a full verb meaning "receive", its object (and only full verbs can take an object) must be some form of noun and followed by a を. The 家まで届けて is not any kind of noun phrase. It cannot quite work like "home delivery" does.
So the first one, where the もらう is correctly interpreted as a subsidiary verb, is the right one.
It is possible, however, for the もらう in the string ～てもらう to be a full verb describing a distinct act of receiving something, as in relatively rare cases where the object of a もらう that follows another verb is omitted. For example:
お砂糖が切れていたので、お隣に行ってもらってきました。"I was out of sugar, so I went next door and got some.")
「Verb in て-form + もらう」
always means:
"to have someone (verb) for me (or whoever that is being talked about)"
It is that someone who performs the action described by the verb and the other person (I/you/he/they, etc.) is the one that receives the service/kindness.
Thus the sentence in question means what your first translation says.
If you see/hear the phrase:
「Noun + を + もらう」
it means "someone receives something". If what you receive is a service instead of a thing, you cannot use 「～～をもらう」.
For example, I just returned from my lunch at a steak restaurant. When I paid at the cashier, the clerk game me a free coupon for all-you-can-drink softdrinks that I could use next time. If I were to tell someone about this, I might say:
「ドリンクバーのタダ券{けん}をもらった or もらっちゃった。」
(「ドリンクバー」 means "all-you-can-drink softdrinks" and 「タダ券」, a "free coupon".)
〜てもらう means to have something done for you.
友達に質問を先生に聞いてもらいました。 (I) had a friend ask the teacher a question for me.
The meaning of receiving something is more explicit with を.
先生はプレゼントをもらいました。 The teacher received a gift.
