Properly speaking, you don't need any power tools to build a cabinet. (However, that would be tiresome to say the least.)
Yes to the router, no to the router table (unless you commit an entire 4x8 sheet to the table), and an additional "yes" to a circular saw with a home-made cutting guide. This picture from woodmagazine.com:
They specify 1/2" stock for the guide; if you ever plan to cut down 1-3/4" exterior doors, then you might (depending on the design of your saw) find your cut depth too small. I used 1/4" for the bottom plate and it works well.
Additional tools that might improve your life, with my off-the-cuff rating scale of 1-10 in terms of bang for the buck: impact driver (7/10), biscuit joiner (3/10), chop saw (3/10) and pipe clamps (9/10).