1) There is always a persistent sodium current which is slowly inactivating in comparison with the fast transient sodium current that occurs when a neuron is depolarized. The effects of this persistent sodium current brings the resting membrane potential near the threshold. Furthermore, neurons do indeed fire and reach depolarization state due to these fluctuations in membrane potential, but those action potentials will not always cause a depolarization of the post-synaptic neurons, since those neurons have inputs of convergence from inhibitory neurons that produce inhibitory post-synaptic potentials. There is no moment or situations where all of your neurons are quiet.
Further information about persistent sodium current can be read in French et al.,1990., "A Voltage-dependent Persistent Sodium Current in Mammalian Hippocampal Neurons"., J. Gen. Physiol., Vol 95;1139-1157 http://jgp.rupress.org/content/95/6/1139.full.pdf
2) The brain center which is thought to play an important role, not only in decision making, but also in behavioral control of the decision making dependent on the reward and outcome, is the prefrontal cortex. Except for its associative learning capabilities prefrontal cortex is thought to have neuronal connections with many part of other brain structures and it must first gather information and integrate the information before deciding what to do. In your question the reward is the glass of water, the emotional response you would get to drink that cold water would aid to the decision making, and the motoric movement is initiated by the subsequent firing of neurons when you see the glass of water and when you recall/remember the feeling to drink it. Prefrontal cortex is therefore activated and can thereafter send action potentials to motor cortex and then to your peripheral nervous system and muscles, so you can pick up the glass of water.
More about this here: http://ac.els-cdn.com/S0959438800001926/1-s2.0-S0959438800001926-main.pdf?_tid=83268f2a-eed1-11e4-ae1f-00000aab0f6c&acdnat=1430354614_ddc06d6aeae4543af28ebe02e29486cc