I'm interested in algebraic geometry (I'm working through Ravi Vakil's notes and also have worked with curves and general varieties in the past), and I have seen some basic definitions from differential geometry, e.g. vector bundles, (co)tangent spaces, differential forms. However, I don't have great intuition for such objects and as a result I feel a bit hindered as far as developing good geometric intuition in AG.
Are there any suggestions as to resources I can look at for efficiently gaining a solidly intuitive, but not necessarily deep, understanding of differential geometry specifically for the purpose of motivating related ideas in algebraic geometry? Or, perhaps, is it essential that I learn differential geometry as thoroughly as I can before trying to study algebraic geometry seriously?