Translation:I will buy them
I grew up in England in the 1970s and we considered "I/we shall" old-fashioned then. But at least you would get my dad's joke sentence, "I will drown and no one shall save me". That would have meant "Leave me alone to commit suicide" in his day (the 1940s), but even he thought no one really speaks like that. (The theory was that if you want to be rescued, you should shout, "I shall drown and no one will save me".)
It means "I will buy THEM" (the things in noun class 10 that we are discussing). They are the direct object.
Your other alternative would mean that the prefix zi- was the indirect object ("buy FOR THEM"), but you would have state what you will buy for these things in class 10.
Nitampa Juma mbegu zake. Ataziuza. = I will give (TO) Juma his seeds. He will sell THEM.
(Juma is the indirect object and the seeds are the direct object.)
This is explained in this lesson (scroll down to Direct and Indirect Objects):