Two methods of getting closer to wildlife are by authorised jeeps and elephant backs. The jeep can be booked at government kiosks early morning, where you might probably find the driver to be accomodating and getting all premissions done by himself. You may as well request to get that jeep for the afternoon ride as well and plan accordingly.
The planning is better done before you start your safari, not just for the lunch breaks and timings but as well as the parts you would like to visit. The Central and western park can be visited for spotting rhino, elephants and deers, which are in abundance. The tiger can as well be spotted based on few other factors apart form luck, e.g., the timing of the year like February would be ideal as well as early morning and late afternoon are time you should be inside Kaziranga on a Jeep.
The Western park is usually meant for migratory birds and the ideal time to visit the place is during the winters and the trip could be a little longer than the other sides but the gear you might need to satisfy yourself are a good pair of binoculars, if your other financial responsibilities hasn't eaten away a zoom lens for your camera.
The Forest Range officers are as good as anyone on this earth to help you plan your stay as well, the best part being they are approachable. In case you are not of the metal to talk to any Government officials or cannot bear the sight of them, the second best alternative is the jeep kiosk where you can as well gather information.