Agree with Iceman.
Take what you can for the moment then later you will need to drop the non essentials.
The strongest Melee class is Teras Kasi. For PvP I would say Fencing ranks second but after grouping with a Novice TK (no skills at all in TK just novice rank) and seeing what damage she could do I have no doubt, anymore, what the Hype is about. I expect they'll take whooping from a Nerf bat sometime soon.
Don't worry too much about what is currently strongest as they should all get rebalanced sometime. Go with what you want for your character. Just because everyone says TK's "own" doesn't mean you can't beat one as a Pikeman, Heavy Swordsman or Fencer.
If you intend on going Master Brawler (or decide to follow the crowd and go TK) get yourself a set of Vibro Knuckles. Speed of 2.5 - 2.1 unsliced then get them sliced, any luck and you'll get a speed decrease. Even when uncertified you will attack faster with them, don't ask why using a weapon makes your fist faster
it just does.
For the order you do things in your elite profession that is entirely upto you. If you're going for Master I would say it is better to do the Rows first (Intermediate, Advanced, Expert, Master) than concentrating on one column at a time. The far right column is always based on Combat Exp so is kind of a freebie as you earn this when you make any exp involving combat.
My Master Brawler/Fencer;
Master Brawler
Fencing 3,4,3,3 (so far)
My Chosen profession Novice Marksman
Rifle IV
Novice Rifleman
For completeness and character Novice Scout
Explorer IV
Hunting IV
Survival II
For the movement, camps, creature knowledge (and character background) Novice Medic
First Aid III
Essential for solo'ing, IMO. Will also make you very useful when in small groups I will need to drop Some of my Scouting skills to finish Fencing and get some points in Rifle. I am also thinking of getting TKA Novice for the Meditate skill.