Let us consider a heart disease data set with 76 attributes. After preprocessing, classification is applied with suitable classifier. I am asking shall we go for deep learning for classification.
It really depends! You mentioned 76 features, but how many rows of data do you have for those 76 features? Also, what is the nature of the data (i.e., pixels/imagery, numeric, enumerated text, dates, etc.)? Once the nature of the data has been understood, and enough data is available, then you for example could consider LSTM or RNN if the data is time dependent, or CNN if the data is image related (these are only a simplistic suggestion).
Of course the question remains and for that extra understanding of the data has to be done: how do we know if deep learning suitable for this dataset?
To answer this question you can obtain a random sample of your data, say 10%, and run a cross-validated deep neural network classifier, XGBoost classifier, a vanilla artificial neural network classifier, and perhaps an SVM classifier. Depending on the understanding of the data, maybe a logistic regression would also do. Then check out the model that has given you the highest AUC ROC. If deep neural network classifier was the highest, then you go with it for the rest of your data.