Please help me buy a computer for school

Please help me buy this computer, I am not able to afford one without help at this time, my current computer is an all-in-one gateway with 1GB of ram, <500GB of storage, Windows 7(nothing after it, just Windows 7,) Intel Celeron 2.7GHz.  Please help, I'm trying to keep up with projects and research, whenever I open the internet and try to do some work it just gets frustratingly slow and eventually overheats. I have to walk eight miles a day to get to a library for one hour, just to do research and projects. This will be a family computer so that they can use it too. 

Thanks, 

-Austin