In your price range I've never seen anything. The only board I know of is the DGT and we're talking close to $1000.
http://www.wholesalechess.com/shop/chess-sets/electronic-chess-sets/dgt-electronic-chess-set
electronic board that records notation
Sort:
Couldn't help but notice slay the Sicilian in there. Play the mainlines, it's what people who both play the Sicilian and those who memorize best play against offbeat lines both fear. 2.f4 isn't going to be too useful for you if your opponent memorizes and understands the concept behind the Tal Gambit after all 
No offense meant here but I can see electronic boards like that being abused by cheaters.
I am looking for an electronic board that would automatically record moves. If it recorded on a flash drive or memory card in pgn format, that would be great.
It wouldnt need to analyze, just record.
Does such a thing exist? (for under $250)