Use Total Commander.
<Ctrl-L> gives you the total size for selected files/directories. You can sort your selection, edit it, and a ton of other features.
In your case specifically:
(Preliminary) size of entire directory:
Hit 'Ctrl-L' on the directory
Now go into that directory and search all files, unlimited depth:
Feed to listbox:
Now select all (make sure you have Configuration/Options/Operation/Select files only checked), then deselect the file types (assuming that what you describe as types can be matched with extensions) you don't want:
which leaves you with
and now you can copy these to the left side.
Free with a nag screen, or $44 / €32 for a lifetime license.