Types of receptors on a single synapse or neuron
One synapse can have different types of receptors for the same neurotransmitter (NT) (example: Glutamate - most glutamatergic synapses have both AMPA and NMDA types of receptors). Synapses can also have receptors for different neurotransmitters (see link).
One neuron can also have different types of synapses which operate with different NT. An example of that would be shunting inhibition, when first comes excitatory synapse (NT - Glu), which depolarizes the membrane, but AP propagation is stopped by the inhibitory synapse (NT - GABA) which comes later. 

Hope it helps, I am also just a beginner :)