How to stop a metal table from vibrating when bumped

Using two legs at a "T" will result in a table that is very prone to tipping. In the diagram below, the sum of the moments (torque) about the R1-R2 axis must be zero for the table to remain in equilibrium. Just before the table tips, all the reaction force from the legs against the floor will be concentrated at R1 and R2.

If the weight of the table at the centroid contributes to a greater moment about the axis than that from a downward force at AB, the reactions from the legs will be distributed more evenly than just the tipping point at R1 and R2.

If you're dead set on a "T" table leg configuration, consider making L1 and L2 the entire length of W and H respectively. That's not enough to achieve stability however, since the far corners of the table are still at a much larger distance from the R1-R2 axis than the centroid of the table is. Therefore, consider trimming the table down to a trapezoid or triangle, with the narrower end corresponding to the bottom of the "T". Otherwise, consider an "H" or "X" configuration for the legs as @Wayfaring Stranger suggests.

90 degree planks will be plenty strong assuming they are not super narrow. Without knowing the details, it's not possible to suggest the best connection. You will want to connect to whatever member has the greatest vertical depth for maximum stability. Do everything possible to ensure the legs are rigidly attached. Nails or screws alone may not be enough. If possible, slightly rabbet the legs into something. The rabbet does not need to be very deep to help significantly. Of course, the fit needs to be fairly snug to be of benefit. Also glue the joints unless the need for disassembly is important. Common woodworker's glue is adequate.