Whatever supervised classification algorithm you intend to use, its success depends on the sample's size, distribution, and representation ( number of samples, locations, and covered objects). You can use Random Forest, Support Vector Machine, Artificial Neural Network, or the newly implemented deep learning SO-UNet that does not require large or complicated samples check
Article Self-Organizing Deep Learning (SO-UNet)—A Novel Framework to...
Any supervised classification algorithm you used, its success depends on the number of samples, locations, and covered objects. You can use Random Forest, Support Vector Machine, Artificial Neural Network.
You can use random sampling method in google earth. Use same temporal range google earth image for that. First you can mark LULC types ( water bodies, built up areas,vegetation areas...) as points or polygons using google earth. Then you can export the data as training samples for supervised classification.