I was checking shutterstock.com and it has these 3 kinds out there -
My initial idea was to just buy the photos and give it to the designer, so he can design the pages around that theme.
I want to get a picture which becomes the logo or front face of the site.
However I've never done this, hence confused by these formats. Can someone help me understand the differences and which one's are preferred for logo/theme.
Save Time. Ask the Person who does the work. Ask you designer what (s)he wants. These different formats are different. They have different purposes and use. If it is a world that you are unfamiliar with -- then get it right from the designer.
You will find this a good strategy for management of vendors, employees, partners, etc. . . .push the decision-making as close to the "worker bee" as possible.
Vector for a logo. This will enable the designer to resize the logo as needed. Vector files are typically created using software like Adobe Illustrator or Corel Draw.
You definitely want the logo designed with vectors, and if possible get the final files to you delivered to you as vectors too. That way you have the most flexibility for usages in the future in terms of size and future redesign.