What are the radio characteristics of communications between tower and aircraft? I have a few questions on the types of antenna used for tower-aircraft comms.

What type of antennas are used today for tower-aircraft comms? Are they directional or omni-directional? 

What's the range of data rate (in kbps) that these antennas can provide? 

Also, is there any safety issues related to power transmission between tower and aircraft? What's the power limit for this transmission? I know that the tower controls the plane until the cruising altitude and after that it hands it over to enroute. Before enroute takes control, how does the tower ensure that the transmit tower is not too high while ensuring it can still reach the plane?
They are omni-directional:  Anyone, in any direction, can hear the broadcast.

They are analog (non-digital), AM signals, so there are no bits, and thinking in terms of kbps or data-rate doesn't make sense.

These have similar transmission power to many AM radio stations.  Do you have safety concerns about local AM radio stations that broadcast baseball games?

Finally, the tower does not "control" the airplane.  The pilot on-board is the one in control.  The tower may simply give traffic directions, such as what heading to take, or what altitude is appropriate.