Electropositive compounds will more easily donate their electron (i.e. reduce)
Electronegative compounds will more easily accept an electron (i.e. oxidize)
Electronegativity increases as you go right and up in the periodic table. (So O and F are very strong oxidizing agents)
Electropositivity increases as you go left and down in the periodic table. (Li and Na are thus very strong reducing agents)
When an acid donates a proton, H+, this proton is reduced to H2(g), meaning the other compound is oxidized, because it has lost electrons to the proton.
NH4+ is an acid and N is fully reduced, so this is probably a better oxidizing agent than Zn which is usually converted to Zn2+, thus being a reducing agent.