Indeed in exothermic reactions the reactants are less stable than the products. Exothermic reactions give off net energy (although not necessarily useful energy), but still require some input energy initially (activation energy). Combustion of gasoline is a very exothermic process, but still requires some input energy. An open source of gasoline does not spontaneously combust in air.
It is difficult to just look at a chemical reaction and determine the enthalpy change associated with the reaction. There are trends though. Combustion is exothermic, melting and boiling are endothermic, and freezing and condensation are exothermic (almost always). Enthalpy of dissolution for solids tend to be all over the place and it is tough to determine whether it is positive (endothermic) or negative (exothermic). Note that just because something is soluble (solubility rules) does not mean that it has an exothermic enthalpy of dissolution. Hope that helped.