I won’t go through a long tutorial about this as there is a Common Setup tutorial for thumbnails. However, the Purified theme has an extensive group of thumbnail crop settings to choose which ones you want to make.
Thumbnails for the Blog: If you know what blog layout you want to use, only check the box next to that blog thumbnail option and leave the others unchecked. For example, if you are using the Grid blog layout, check that box only.
If you decide that you want cropped images for your Recent Posts widget, Related Posts, etc., enabled those ones too.
CAUTION: Only enable the thumbnail crop settings that you need. If you turn them all on, every photo you upload will have a copy for each size created. This will eventually fill up your host server space.