Answer the following questions and you should then know what to do.
- Where is the Internet router located in relation to where the iMac will sit?
- If they're in different rooms, how will they connect? Is the house already wired? If so, what level of cabling?
- What other ethernet wired devices are in the household? Do they have a NAS? Another computer they'll share data with?
- What is their Internet speed? Gigabit? More? Less?
- What is their typical online activity? Does it require a lot of bandwidth (how much?)
I'd suggest that if the imac will sit right next to (or on the same wall as) the router, sure get the ethernet option. If they're in different rooms and the house is already wired for ethernet with cat5e, sure go for it. Otherwise, plan for wifi. Won't hurt to buy the ethernet option but don't go into contortions trying to do a wired connection unless you find you truly need it.