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It depends on what platform you plan to use. If you want to get a new phone, you need to choose between Gear or Daydream, unless you get Samsung S8/S8+/Note 8 which should be compatible with both platforms.
I do have a list of Gear/Daydream compatible phones that I collected from their official websites. You can look around for the prices.
I am not really sure about the price of some other phones, but you might be able to find some tips online. Maybe Youtube or Reddit?
However, honestly I do not think you will get much of an ideal VR experience out of a smart phone with 200 dollar budget. The resolution/framerate/processing power just will not be good enough.
What I suggest is that you wait for a bit longer for either price drop on these listed phones, or the MX/standalone headsets that are coming out this year from many manufacturers. Some of these things run on your PC, so they are relatively cheaper than smartphones that are compatible with VR and they sometimes offer a better/smoother experience. Others are completely independent devices but should still be cheaper than top end smart phones(I guess..). But then you will not have an extra phone if you choose these.
Hope this helps Happy new year.
Here are two lists of phones that are compatible with Gear VR and Daydream:
Galaxy S7 edge
Galaxy Note 5
Galaxy S6 edge
Galaxy S6 edge+
Galaxy Note 4
Galaxy Note 8
Galaxy Note 8
Moto Z Force
Moto Z Force (2nd gen.)
Mate 9 Pro
Porsche Design Mate 9