How to decide the processing power required based on the dataset?
Dataset (number of samples, number of features) is one variable. Algo/model complexity is another. 

For example, linear regression will be much faster as compared to 4 layer neural network (and will require much lesser compute power).

So, before deciding need for compute powers, you can : 


Try few models with hardware (or AWS instances) you already have 
Estimate need for better hardware (CPU / GPU) based on the performance and what is the bottleneck 


For very large data sets (say 10 TB+), I/O can become the bottleneck.