You shouldn't confuse GL_ARB_pixel_buffer_object with the old (and quite horrible) pixel buffers which were used for render-to-texture before FBOs were specified (and which once had the distinction of almost driving John Carmack to switch to D3D). GL_ARB_pixel_buffer_object is something quite different.
If you support GL_EXT_framebuffer_object but not GL_ARB_framebuffer_object a simple driver update might be all you need; otherwise you're very probably on extremely old hardware. If that's the case then GL_EXT_framebuffer_object is the one you want (but if you ever upgrade be careful not to mix -ARB code with -EXT code or things could get weird on you).
An older trick that's compatible all the way down to GL1.1 is to use glCopyTexSubImage instead. It uses up more bandwidth of course, but that's the tradeoff. The basic setup for your requirements would look something like:
At program startup:
- Create an appropriately sized texture (using a NULL pointer for data).
- Clear the screen to black.
- glCopyTexSubImage to initialize the texture to all-black (the driver should automatically do this with a NULL pointer but some might not).
- Draw your appropriately-sized texture as a fullscreen quad.
- Draw your objects.
- glCopyTexSubImage it again.
This way your appropriately-sized texture becomes a running copy of the previous frame's contents which forms a baseline on which to build the current frame.
As for the size, it should be at least large enough to cover your screen dimensions, which may be a non-power-of-two. If you don't have hardware-accelerated non-power-of-two support look at GL_ARB_texture_rectangle which will let you create such a texture but with some limits (which shouldn't matter in your use case).
Of course another consideration is that your hardware should support such a texture size, but so long as you can do 2048x2048 you should be OK as that'll cover most resolutions.
If that doesn't suit you, you can also do something with the accumulation buffer, which goes down to OpenGL1.0 but may not be hardware-accelerated in some cases.
Plenty of options!