Another option is to install the Anaconda PythonAnaconda Python distribution which has packages for GDALGDAL. If you are going to be doing a lot of work using GDAL with other Python packages (scipy, pandas, scikit-learn etc.,) this might be a better option than OSGeo4W. On the other hand if you want to use Python in combination with a number of open source-source remote sensing and GIS packages (GRASS, QGIS etc.,) OSGeo4W is probably the better option.
You can get the full Anaconda distribution from: https://www.continuum.io/downloads which contains a lot of Python packages aimed at 'data science' or a minimal installation from http://conda.pydata.org/miniconda.html
As part of the installation it will prompt you to add to the main path (so it is available from any terminal).
Once set up GDAL can be installed into a new environment using:
conda create -n gdal_env -c conda-forge gdal
Then activating it as showshown when the command finishes. Installing into a new environment is recommended to avoid conflicts with other packages and make sure the environmental variables required are set.
I've suggested installing from the conda-forge channel (https://conda-forge.github.io/) as they are very active in keeping their GDAL builds up to date and making sure they work against a lot of libraries.
Once installed packages can be updated from within the environment using:
conda update gdal