So I did get a few Op-Amps but absolutely failing at getting the circuit to works, I just don't get any amplification.
I'm currently trying to use this (seemingly common) circuit:

http://hyperphysics.phy-astr.gsu.edu/hbase/electronic/opampvar2.html#c2
Maybe I need actually negative voltage on V- and not ground?

Though I did get a few better results by using a 1k resistor instead of a 33ohm one. 33ohm assumes 100A which is just bullshit in this application, I dont want to measure a whole house hold just one appliance which can't draw more than 16A. Considering the washing machine I test with is also far from using 16A I opted for around 3A. Though the result is still not satisfying, beginning and end of a run is still not spiky enough to have an easy to write code to detect it. The noisy part at the front and end is how the current usage looks like towards the end but the noise also appears sometimes when idle.