What causes the preliminary changes in resting membrane potential in neurons?
You have already listed two possibilities:


  1) mechanical changes (stretching, pressure, etc)


and


  3) Ligands (neurotransmitters, etc)


In the central nervous system, ligands and in particular neurotransmitters are going to be the overwhelming cause of most initial depolarization. Ligand-gated ion channels are the simplest mechanism: some examples include AMPA receptors, GABA-A receptors, and nicotinic acetylcholine receptors, but it is also possible to change the membrane potential via second messenger systems that open or close other channels.

In the periphery and in sensory organs, sensory-evoked potentials can be caused by mechanical gating, as you mention, as well as by specialized channels that respond to particular stimuli, for example the TRP family which includes channels sensitive to temperature (for example TRPV1, which responds to heat and also responds to capsaicin, the chemical that makes chili peppers 'hot') and to certain chemicals in food (resulting in taste).

The other category you missed is that some cells generate a spontaneous depolarization because they contain channels that are activated around the resting potential (and/or potassium channels that close, which also depolarizes the membrane). This is crucial for the cardiac pacemaker but can also be found in the central nervous system in some cell types.