Let me just start by saying, I Love Brand. He is the only champion that I never get bored of, and find a wonderful level of satisfaction in playing because of his skill set.

The satisfaction you get from landing all 3 skills shots procs his pasisve which is like the game is rewarding you for it, like hitting the jackpot on the pokey machines.

Liandry's Torment and Rylai's Crystal Scepter are essential items to pair because the slow from Rylai's Crystal Scepter causes the Liandry's Torment passive to proc double damage over 3 seconds on top of that they are dealing with your burn passive at the same time when your ulti is fired on a group of low hp the added bonus from COUP DE GRACE will give easy penta's

You want to max his "e" as soon as possible this skill is the easiest to land and sets up for your q to stun or your "w" which will do extra damage if they are already ignited.

Best way to farm is to land your "q" on the siege minion "e" him to spread it then aim "w" front and back minions. Another option if no siege minion is to use w on everything then "e" the the center most minions so it spreads to all after that you can pretty much 1 shot auto the casters then by that time the melee minions will be ready to be auto'd

WIll update more shortly