Step 1: Know the rule.
For oxides of the same metal, the lower the oxidation state of the metal, the more basic the oxide. As the oxidation state rises, the oxide becomes acidic.
Step 2: Find the oxidation state of Mn in each oxide.
In \(Mn_2O_7\), Mn is \(+7\). In \(MnO_2\), Mn is \(+4\). In \(MnO\), Mn is \(+2\). In \(Mn_2O_3\), Mn is \(+3\).
Step 3: Compare the oxidation states.
The smallest oxidation state here is \(+2\), which belongs to \(MnO\).
Step 4: Decide the most basic one.
Since lowest oxidation state means most basic, \(MnO\) is the most basic oxide. \(Mn_2O_7\) with \(+7\) is in fact strongly acidic.
Step 5: Conclusion.
Arranging by basic nature: \(MnO > Mn_2O_3 > MnO_2 > Mn_2O_7\).
\[ \boxed{MnO} \]