Hi blueroomelectronics,
The type drill press you provided in the pic is not a good choice for PCB drilling.
Remember, when looking at a press other than a dremel always firmly grab the chuck (jaw) and shake it to feel if their is ANY horizontal movement.
Typically, PCB drilling requires an index from #55 - #60 which are extremely thin bits/rasps.
Any horizontal movement concerning the chuck can easily cause a distorted hole.
The picture you provided (drill press) is more oriented to chassis hole drilling etc...
A dremel is the perfect drill for PCB use since the chuck is directly connected to the motor shaft.
Furthermore, purchase the dremel press since it is matched for the dremel drill!
Honestly, i like to use a dremel off of the press (hand use) since i can achieve a good feel for required pressure.
However, if you plan to use a dremel (hand use) always make sure your drilling is a straight pass through the PCB, avoid any angle etc...