They are both correct and used in written and spoken Polish. I think the infinitive form was considered wrong in the past, but now it is legit :) The construction with infinitive is more simple, as it is gender neutral. Maybe your book forces you to use the past form of a verb, so you can learn genders better?
Rules of Polish language state* that you can't use infinitive with modal verbs, so „będziesz móc mieć”, doesn't exist and in such case the only option is past tense form, so either „będziesz mogła mieć” or „będziesz mógł mieć”(ie. we avoid double infinitive).
Other than that, both forms are equally valid. The infinitive form is actually older and comes from Proto-Slavic and in many Slavic languages is the only option for future tense; the to be + past form is a later Polish innovation(and I think it also spread to Kashubian, but I'm not sure).
* – At least according to poradnia PWN.
It doesn't clear up much. In Polish "Czy zamierzasz to jeść?" would mean something like "Are you you really sure that you are going to eat it?" so I would rather say "Czy będziesz to jeść?" if I want to simply ask. "Czy zamierzasz (or better: "planujesz") mieć nowy komputer?" would mean "Do you plan to have a new computer?". Would you use "going to" then?
I'm fairly sure I've heard Irish English speakers use the rare Future Continuous form "You'll be having a..." to mean "You will own a...". Without the Irish accent it sounds rather quaint, however, so most learners of English as a foreign language will prefer to avoid it.