In order to amplify sensitive, high-impedance sources, you could do the following:
simulate this circuit – Schematic created using CircuitLab
- make sure the biasing of the piezo output doesn't load the piezo too badly
- use a high-input-impedance opamp configuration to amplify and more importantly buffer the signal
- use a local supply with a modern LDO to minimize noise that gets coupled into the supply line of your cable
- use a termination resistor in the order of source impedance (i.e. output impedance of your opamp) to make sure energy is actually sunk into your MCU end, and to load the virtual noise current source.
- Use microphone cable, which is a shielded thing – it even exists with two cores (one for 5V, one for your signal, GND on the shielding).
If you don't need gain, you can omit the R4-R5(C4) virtual ground, and R3-R6, and just replace it with a straight Vout->V⁻ loopback, giving you a unity-gain voltage buffer.
The current I in the above schematic is the sum of the current needed to create the two virtual grounds (R1-R2 and R4-R5; the latter clearly dominates), as well as the supply current of the opamp, which itself is dominated by the current it sinks into Rterm.
So, rough calculation, it's 3.5 mA for the biasing and less than 3.3 mA that can be sunk into Rterm, so about 7mA in total.
That means that you could add 100 Ω in series with U1's input, should you need more supply voltage noise reduction. The resulting voltage drop would still allow U1 to stabilize its output.
The question whether TLV07 is an appropriate opamp is hard to answer. Generally, an opamp with a lower output impedance would be desirable, but that usually comes at the cost of lower input impedance or higher noise. However, using a stronger driving opamp would allow you to reduce Rterm, e.g. to 50Ω, and that would greatly improve noise immunity. It's all a trade-off.