A fine natural bristle brush is best, however, any good, fine bristle brush will do. Please do not use an ordianry furniture finish varnish for your project. Here in the U.S., the clear coat of choice would be either Spar Varnish or Polyurethane.
I just completed refinishing a cedar outdoor bench for the garden using spar varnish. It's the second time I've refinished it and the last one looked pretty good for about 4 years through all kinds of weather.
At least two coats between which one uses fine steel wool to smooth the suraface.
Best of luck!