The Millennium eOne chess set is probably in your price range but it is smaller than regulation. I would not use the same board to play OTB as well (increased risk of damage with the transport and someone else playing on the board), especially as an OTB set won't run you very much money at all (I use the standardized playing mat which I got for like 10 bucks).
Cheapest Electronic Chessboard that works on Chesscom
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I've been looking for a great board that I can use to play OTB and will show up on screen while streaming or studying. I'm looking for something around the $150 range (max $200). I don't need anything fancy or big, just something I can connect to chesscom without issues. If you have any suggestions, I'd love to read them!