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The best companies to give you the desired experience will be the top ones in your career field.
Altough, in case you are looking for an internship in business industries I would definately recommend the multinational companies which have more structed Internship Programs. Some of them also have leadership programs after internship, which is a great way to develop leadership careers.
I started my career as human resources intern at General Electric, where the dinamic and complex environment really helped my professional and personally development. I had many responsibilities, had-working task and attended many courses. All this mixture were key for being prepared for the next levels.
Look for the opportunities that will challenge you - those will give you the best experiences you can have.