Your brother and father would be expected to have identical results so you only need to test one of them. If your brother is happy to go ahead then use his DNA. It's best to start with the Y-DNA as the results are easier to understand and have more value for your genealogy research. What you'll get out of the test depends on your brother's surname and how many other people with the surname have been tested. Most of the surname projects are at
www.familytreedna.com. If there's no surname project you can test with a geographical project (FTDNA have projects for Devon, Hampshire, East Anglia, Wales and even a catch-all giant project for the British Isles). The larger the database the more chance you have of getting matches. There are some surname projects too which will offer free or subsidised tests, and especially those with established surname societies or with large numbers of American testees where resources can be pooled.
With the mtDNA, you have inherited the mtDNA from your maternal grandmother so again only one test is required. If you were both tested you would be expected to have identical results. mtDNA gives less precise results, and the database is smaller, so it's better for learning about your deep ancestry. If you've been following "The Incredible Human Journey" on BBC2 you'll have seen that most of the early part of the journey has been tracked genetically by mtDNA.