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:
- Paladin: Sword of Justice 1/5
- Shaman: Doomhammer 2/8
- Warlock: Lord Jaraxxus 3/8
- Rogue: Assassins Blade 3/4
- Paladin: Light's Justice 1/4
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.
It says
Look at the top tree cards... Draw one...
Having 2 cards left, you would look at the 2 of them and pick which one to draw and discard the other, no fatigue taken.
Having 1 card left, you would look at that card and draw it, being the lone card left, there's no option for you to choose from. No fatigue taken either (as Studoku confirms in his answer).
Having no card left, you don't take a fatigue hit, since you can't look up at any cards, you can't draw one, no fatigue.
As you can see from the screenshot of my testing, my health haven't changed after playing the second one with no more cards.
Looking at cards doesn't count as drawing them, neither is discarding them considered a draw attempt.
Note that fatigue is represented as a card but it's not a card at all, it's just the way Blizzard decided to represent it. It could have been a stabbing dagger, a chicken biting you or whatever... so don't mistake the look fatigue got with it being anything but a effect of having no more card and having to draw one.
Best Answer
I tested this out with 'Molten Blade', 'Shifter Zerus' and 'Shifting Scroll'. In all 3 cases you get what the card is currently turned into.
In this case Zerus turned into an Ancient of Lore and Molten Blade into Glaivezooka when I shuffled them in.