What I want to do now is erase the part of the torus mesh that is inside the cup, I tried joining the cylinder and torus but that didn't help much (Why would it help anyways). How can I delete that unwanted part? B-Selecting/Deleting vertices isn't very efficient and easy to work with.
Know all the mesh selection tools.
Other mentionworthy tools:
Expand Selection - ⎈ CtrlNumpad+
Reduce Selection - ⎈ CtrlNumpad-
Select Edge Loop - ⎇ Alt RMB
You could also use a boolean modifier.
Select the torus and apply a boolean modifier with the cup as Object and the Method to Difference. Apply the modifier. Now you can use the Select Linked Tool L to delete the unneeded vertices.