I would paint models after building as much as possible without covering the hardest places to reach because it makes it easier to paint everything at once. I would advice you to do the same as it's far less likely for your kit to have uneven paint job if you paint every part at the same time.
Spray painting is probably the best method in applying a base coat as it's the quickest way to cover your model with an even coat of paint. And when painting in the proper colours, just make sure the paint settles evenly, and if there are some places uncovered let the paint dry first and apply a second coat later.
Remember to thin your paints.