osu1991 & CochiseGuy pretty much covered the questions. I needed an outdoor antenna (45-50 miles from my Wash DC locals). I used antennaweb.org to find the distance & direction from where I live. I can't really remember, but my OTA antenna + a pre-amplifier was probably a little less than $100. I did all the work myself - depends on how willing you are to climb up on the roof & mount the antenna - if you are not comfortable with that kind of work, I'd hire someone to do it.
As far as using it as a 3rd tuner - it's all built into the 622. Once you have the antenna & "scan for OTA channels" on the 622, the OTA channels will appear right in the program guide. For example, my NBC OTA is channel 4 & in my program guide, I have:
004-00 = Local NBC channel 4 HDef from Dish Satellite
004-01 = Local NBC channel 4 HDef from OTA antenna
004-02 = Local NBC channel 4 digital "subcarrier" channel w/the weather forcasts
So the antenna stuff is pretty seamlessly integrated into the 622. When you want to record something, you can choose either the OTA or Satellite channel.