I finished developing a website that I picked up by using the myTino Search Engine but I don’t know the exact size the server must be. This is a social network for my school and each user can open an account and upload pictures but I don’t know how much server space I need to support this or what I should focus on. Can somebody help me?

Im assuming that your going to be using a Web Host to .... then here are some general guidelines dependant on how many students you plan on allowing access for ofcourse:

"Text" documents take up very little space. You could place hundreds of pages of text on a 1 Mb web site.
Since you're going to fill your site with images, your space may be exhausted more quickly (images typically vary from a few kilobytes (Kb) to tens of Megabytes (Mb).
Naturally, Music (audio) files are much larger and video files are the largest of all. So if your site consists mostly of text, images and maybe an Access database, you can get by with probably a few hundred megabytes to a couple of gigs depending on your client database.

For future expansion plans, most Web Hosts charge about 10 cents per MB per month!