The past continuous tense expresses an unfinished or incomplete action in the past.
The most common use of the past continuous tense is to talk about something that was happening around a particular time in the past.
It is also used to describe an unfinished action that was interrupted by another event or action, e.g. "I was having a beautiful dream when the alarm clock rang."
Whereas the simple past tense, is used to talk about a completed action in a time before now.
We often use the past continuous and the past simple tense together. When this happens, the past continuous describes a longer, ‘background’ action or situation and the past simple describes the action or events e.g. "When I woke up this morning it was raining and my father was singing in the kitchen."
Often, the ‘action’ described by the past simple tense interrupts the ‘situation’ described by the past continuous tense e.g. "I broke my leg when I was skiing."
Notice that the past continuous describes ‘situation’ that go on for some time – ‘skiing’ but the past simple describes ‘actions’ that happen quickly – ‘broke’.
For your case both a and b are in past continuous are examples of past continuous and the past simple tense being used together where as c is an example of simple past.
For sentense construction I would suggest to use "was sitting" since it describes the stituation which was happening at that particular time i.e. you were sitting besides your granny.