You can get decent starter kits from home brew shops (try the forum sponsors for a start) which come with all the basic bits to get you going including fermenting vessel, hydrometer, bottles etc... Some you get a choice of beer kit you'd like too. Depending on what you like to drink will obviously depend on what beer kit your want (assuming you drink beer). Look on here for reviews. The Coopers kits are very good for single can kits, there are other very good makes too, plus two can premium kits from other manufacturers are worth a look.
Bottles are the simplest route to take as a beginner, so I would forget barrels for now.
You will need sterilising solutions or tablets to sanitise stuff, but I have used diluted thin bleach for years and years as my path of choice. Don't use thick bleach if you go that route.
You'll possibly need some standard white sugar for carbonating your bottles should your starter kit or beer kit not come with priming sugar or carbonation tablets.
Then all you need is a bit of time a patience.