I have a field with date/time dataType and using that field in VF page, initially date picker was not visible then changed standard stylesheet = "true" (is this the only option) and everything works fine in system view BUT in SF1, datepicker appears in a random manner
You have two options here.
- you can use the SFDC stylesheet to render the fields as per the classic view which will not necessarily work in LEX (Lightning Experience). This is going to be a more limited option as you are at the mercy of Classic styling.
- Roll your own stylesheets using Lightning Design System see here
If you really want your page to work in LEX I would recommend option number 2. If you really want your page to be future proof I would make it out of Lightning Components and expose it in Classic via Lightning Out. The learning curve is definitely steeper here but worth it in the long run.