Choosing transistor for amplifier
Voltage gain for a single bipolar device, with no emitter resistor, is at most VDD/0.026. You want 200, thus you need at least 5 volts. Go for 12 volts. 

For a Rin of 20,000 ohms, assuming Beta of 100, you need reac of 200, which means Ic of about 100 microAmperes. 

To swing the collector voltage by 10 volts at 100uA, you need 100K ohm Rcollector.

To interface that to 50 ohms, you need a lot of emitter followers (CC topology).

Given Rcollector is 100Kohm, and assuming 20pf (two of Cob) on that node, your timeconstant is 2 microSeconds, 500,000 radians per second, or about 90,000Hertz F3dB.

Any small-signal bipolar will do fine: 2N3904, 2N918. Even Nchannel JFETs, if the transconductance is high enough.