Sampling one signal with two separate ADCs at different rates?
If you are really using two separate ADCs (rather than one ADC with an analog mux) then you should make sure that one ADC has finished its conversion before starting the conversion on the other ADC. Make sure that both ADC inputs are driven from a low impedance source, such as an op amp connected as a voltage follower. If you are really paranoid, use a separate voltage follower for each ADC. Use good bypass capacitors for both ADCs and follow any datasheet advice about routing the analog ground vs. the digital ground. You haven't given any indication of your resolution requirements so it's hard to be more specific.

But it's not clear to me why you need two ADCs for the application you've described. Why not just average the samples from the high-speed ADC to compute your low-frequency average?