I believe there are many ways to determine if data is normal or not:
Which of the above is the best way to determine if data is normal and one can proceed with parametric tests?
After going through this thread (Is normality testing 'essentially useless'?) as suggested in comments by @Luca, I am inclined to conclude that:
Formal tests can be misleading (may show non-normal distribution in large sample sizes, even if data is largely normal); hence can be avoided.
Non-parametric tests should be used for small samples. They are reasonably good even for normal data.
Parametric tests should be for large samples. They are reasonably good even for non-normal large data.
qqnorm(vect) & hist(vect) (R commands) plots may be best for graphic / visual assessment.