The question that you have asked has quite a broad answer. I would suggest you to narrow down your question. Even within land use land cover studies you may be interested in a particular land cover or land use type. Is it vegetation - forest, agriculture, urban areas, water bodies that your are most interested in?
Some suggestions from my side. Generally for any remote sensing study it is advisable to first of all think of the specific object on the surface of the earth that you are interested to study and their properties and then look for appropriate tools which will be suitable to answer your research questions. Whether it be for India or any other study area on Earth, the principle remains more or less the same. If you answer the following questions you will be in a better position to find the answer to your own posted question.
1. What are the characteristics of the object that you are interested in studying?
For example, if you are interested in studying the vegetation phenology throughout a year, you may first have to make a careful note of the plantation, growth, maturation and harvest seasons of the particular plant type. You also need to note down the size of the field, size of the plant, type of plant etc. Once you have made a summary of the characteristics of the object of interest you can then move on to the next question. of
2. What tools are available for studying the object of your interest ?
A note here. Landsat is not the only satellite freely available. It is definitely one of the most popular ones because of its historical coverage but there are others like ASTER, MODIS, Sentinel family, Hyperion, etc. Take a look at the following links which I generally use. You will find many other options. There are many other links out there on the web. These are just a few:
http://earthexplorer.usgs.gov/
https://search.earthdata.nasa.gov/
http://reverb.echo.nasa.gov/
3. When you look at any tool (any satellite image ) try to match the Spatial, Spectral, Temporal and Radiometric Resolutions of the satellite with the properties of your object of interest. The one which provides the best match may most probably be the best tool to answer your objective.
James stated the essential things you should consider while planning a remote sensing based study.
This is also important that you should consider the climatic conditions to India, particularly in the study region, in order to obtain the cloud free image for the analysis. As you know our country having different climatic zones..
Like wise if you look you will get very short span of time for obtaining the good images.
For example if you take the southern part of India, the better time to collect the image is from December to April..( slight variation will be there), with less cloud cover and other distortions.
Hope you these answers will help you to plan the work.