What are good representatives for the concepts of endergonic and exergonic? We must demonstrate two reactions: endergonic and exergonic. I'm wondering if thefollowing reactions are accurate.

Exergonic: I have sodium bicarbonate and vinegar. Would it be catabolic, spontaneous, and $-\Delta G$ as well?
Sodium bicarbonate and vinegar is your basic science-fair volcano reaction. You have the baking soda in a container of some sort and pour the vinegar. The formula would be something like
$$\ce{Bicarbonate of soda + vinegar -&gt; Carbonic acid + Water + Carbon dioxide gas}.$$

Endergonic: I have ammonium chloride and water. Would it be anabolic, nonspontaneous, and $+\Delta G$?
Ammonium chloride would be dissolved into the water. The formula would be something like
$$\ce{NH4Cl + water -&gt; NH4+ + Cl-}$$


I've just barely touched on the $G$ value thing. I don't exactly know what's going on there. What I mean I guess is that if it's $+\Delta G$, the enthalpy increases, and if it's $-\Delta G$, the enthalpy decreases. To be more precise, we're on the Gibbs free energy lesson at the moment.
Endergonic means energy is absorbed during the reaction. Exergonic means that energy is released during the reaction. Is energy released or absorbed during a vinegar and baking soda reaction? Is energy released or absorbed when dissolving ammonium chloride and water?
As you say you are starting with Gibbs free energy, just pay attention to the $\Delta G$ values. Remember that $\Delta G= \Delta H -T\Delta S$ so it doesn't depends only on enthalpy but also on entropy. A process where $\Delta G&lt;0$ is exergonic and in the opposite case it is endergonic.

About the examples we can say that: 


Salts that disolve in water are exergonic processes, $\Delta G_\mathrm{disol}&lt;0$.
Sodium bicarbonate will disolve in vinegar to produce $\ce{CO2}$ (because of the high concentration of acetic acid), it is also exergonic.