Yes, that counts as a weapon. Specifically the weapon is a card named "Blood Fury."
If the "weapon circle" is filled up, it counts as a weapon. Anything expressed in the format attack/durability is a weapon, the other effects that can give your hero an attack last a single turn and are just expressed as "x damage till end of turn"
There are 2 great ways you can use Baron Geddon.
OPTION 1 (available to any golden legendary)
Since you got a Golden B.G. you could disenchant him for 1,600 dust which would allow you to craft any other non-golden Legendary of your choice (if you are not a huge fan of him).
I believe most people consider him to be one of the better legendaries, but above him yet is still (definately) Ysera and Ragnaros the Firelord. Leeroy Jenkins can be a great surprise game-closer as well.
OPTION 2
Second, you build him into your decks (some of them).
I do not have one yet, but I have had him work well in 2 arena decks where I had the good fortune to draft him. He is best used in a late-game style control deck.
I believe the best way to use him is in a Mage deck with +Spellpower (2 kobold geomancers, 2 ogre mages, & 2 azure drakes, +Malygos?) and a lot of spells. Arcane Blast, Blizzard, Flamestrike serve to wipe the board, especially with the benefit of spellpower.
In that kind of deck, Baron Geddon functions as an additional board wipe that also puts out a ton of pressure on your opponent's health.
He could be good in a druid deck because you could get him out earlier, also druids can be built with a lot of spells, similar to the mage and he could add additional control. He probably is a little worse in a Warlock deck than in most others because he competes with your ability for your limitted resource of health. He is probably not great for a shaman or paladin deck because he limits the functionality of your ability.
He will not work as well in an aggressive deck that uses a lot of small 2 & 3 cost minions. Try him out in a few different situations and do some unrated games in "Play" mode and report back here and let everyone know what you found out.
TL;DR: My opinion
Mage: +++
Druid: +++
Priest: ++
Warrior: ++
Rogue: ++
Paladin: -
Hunter: -
Shaman: --
Warlock: ---
Best Answer
There are no particular combinations, it depends entirely on whether your opponents play enough weapons for him to be worth it.
Harrison Jones is a 5/4 minion for 5 mana. You can get a 4/5 Chillwind Yeti for 4 mana, which is probably one of the best plain minions. Compared to that Harrison Jones is not a very good minion if you don't get to trigger his special ability. But a 5/4 for 5 mana is also not terrible.
But I think you're underestimating the value you got in the situations where you played him. Even one card drawn and 1 durability destroyed is a pretty good outcome. You denied your opponent card advantage they might have gotten from using their weapon a second time, and you gained 1 card advantage yourself from drawing a card. That is pretty good already.
The situations where Harrison Jones would be devastating would be enemies that use the following weapons:
Harrison Jones is a very situational card. It depends entirely on the current meta and the opponents you face whether it makes sense to use him in your deck. In a very weapon-heavy meta he can be very useful, against a weaponless opponents he's a rather expensive and mediocre 5 drop.