I always add Optifine (http://www.minecraftforum.net/topic/249637-152-optifine-hd-d3-fps-boost-hd-textures-aa-af-and-much-more/) right away, even though I have a pretty decent PC but there are lost of options which can speed up MC without affecting graphics.
Good optifine options:
Performance: Max FPS
Advanced OpenGL: Fast (if availible)
Smooth FPS: On
Smooth World: On
And FPS++ also works well because it uses better cos and sin formulas (http://www.minecraftforum.net/topic/1350464-15fishtacos-mods-fps-lava-decay-fog-key-and-more/)