It is not very clear what do you mean by 'ideal' time interval. The effect of soil moisture on simulated near-surface meteorological fields  will happen very quicky - the order of seconds to minutes (time scale of turbulent diffusion processes in the atmospheric surface and boundary layer). So, if you want to see, how improvement in soil moisture will improve the calculated emperature, humidity, etc in atmospheric surface layer or in atmospheric boundary layer, you just initialize WRF at the very close time e.g. from 1 to 12 hours ahead. However if the purpose is to study how soil moisture effects on meso- and large- scale circulations (and therefore - meteorological fields also at upper levels) then such effects will need more time to come in force. So in this case initialization of 24 hours ahead could be more reasonable. The above answer is just the 'ad hoc' assumption.

Dear Dr. Ivan, precisely I want to study the effect of pre-monsoon surface irrigation on land surface processes at meso-scale (large scale).  The increase in soil moisture is human induced, hence it is not captured by GFS or any other data set used to initialize the WRF model.  I am using satellite derived soil moisture to replace GFS soil moisture values. The question of time interval arises when I simulate the model for longer duration. Then what should be the time interval for soil moisture up-gradation using satellite data and what could be the model response time. So accordingly I will choose a particular time to study the impact of soil moisture on land surface processes.   

would you like to mention the satellite based soil moisture update temporal resolution available? Further, the closer update interval is only computationally expensive otherwise generally it gives better simulated results. In my experience the 24 hour spin-up time is appropriate for 3 to 5 days simulation but yet it is the matter of your domain configuration and grid-resolution and of course your objectives.