The "radio" voice sound is a combination of the mic (the EV RE-20 is a relatively inexpensive option), compression and EQ. Radio stations use "steamroller" compression, which eliminates much of the dynamic range of the sound source, and hypes certain midrange and upper frequencies to give the sound source more "cut".
The era of the broadcast will also determine the sound you are looking for. In the 60's and 70's many AM stations used reverb on the DJs voice (at least here in the NY area). Mic technique is also a factor. Some DJs would "eat the mic" or speak with their mouth very close to the mic (Alison Steele "the night bird" from the mid-70's is a good example), which also creates a very distinct sound, very intimate with lots of low end.