To select between the single quotes I usually do a vi' (“select inner single quotes”).
Inside a parenthesis block, I use vib (“select inner block”)
Inside a curly braces block you can use viB (“capital B”)
To make the selections “inclusive” (select also the quotes, parenthesis or braces) you can use a instead of i.
You can read more about the Text object selections on the manual, or :help text-objects within vim.