Signature generation I am trying to unwrap bitcoin transaction generation process.

A bit confused about signing part.

My understanding is the transaction is sha256'd, then sha256'd one more time, then ECDSA'd. 

Based off https://en.wikipedia.org/wiki/Elliptic_Curve_Digital_Signature_Algorithm, ECDSA will first hash the message. Does that mean the transaction is sha256'd 3 times in total?

All the best!

Johnny
No, only two hashes. The hash itself isn't typically described as a part of ECDSA though the input must already be hashed (because e.g. a signature of 0 is trivially forged).