Best oxidizing and reducing agents: Na, Zn^2+, Ba, Ba^2+, and Ag?
It is a good idea to recap the the definitions of oxidation and reduction when approaching this kind of question, and also what it means to be an oxidising or a reducing agent:


Oxidising is defined as the loss of electrons, reduction as the gain.
An oxidising agent is good at oxidising other compounds while being reduced itself; and vice-versa.


Take another quick look at your list; all you have are neutral elements or the most common cations of said elements. If you want to oxidise or reduce, then we would always be going back and forth between either. Therefore, only sodium, barium and silver are potential reducing agents on your list (being oxidiseable themselves) while only zinc(II) and barium(II) can be oxidising agents. Here are the relevant equations:

$$\begin{align}\textbf{Reducing agents:}\\
&amp;&amp;\ce{Na &amp;-&gt; Na+ + e-}\\
&amp;&amp;\ce{Ag &amp;-&gt; Ag+ + e-}\\
&amp;&amp;\ce{Ba &amp;-&gt; Ba^2+ + 2 e-}\\
\textbf{Oxidising agents:}\\
&amp;&amp;\ce{Ba^2+ + 2 e- &amp;-&gt; Ba}\\
&amp;&amp;\ce{Zn^2+ + 2 e- &amp;-&gt; Zn}\end{align}$$

Using your table or our chemical intuition, we can then decide which reduction or oxidation is the easiest. The best oxidising agent without doubt is zinc(II) as it is much more noble than barium (although still not a noble metal). The best reducing agent is a slightly more tricky call without data, but barium(0) being further down in the periodic table allows us to assume it to be stronger. Luckily, this is supported by the data.