You'll have to figure out how to measure the short-term and long term stability of your reference and Vcc supplies. That's only the beginning but having the correct measurement instruments is essential. Precise measurements of both load current and supply voltage as those loads vary is essential to solid analog measurement system design.

Your measurement instruments' precision must exceed your desired system precision by a factor of 100.

When you design your circuit board, you must ensure that you have, available to every layer on the board, a single-point low-impedance GND. That means a dedicated GND layer as near as possible to the analog circuit layers. You also need a single-point low-impedance Vcc layer so that there aren't any offsets between different Vcc points on your board. The analog reference supply must be carefully protected from noise of any sort or magnitude by that low-impedance GND as well, carefully filtered and decoupled to eliminate contamination with any undesired signal.

Once you have figured out how to resolve those issues, you're well on your way.

RE