Its a dilemma alright. At the very point in the game when are poorly equipped you just have to open a door. This makes early searching very important indeed. It is good to have at least one character with the Search ability. This is a free Search action. This Survivor can help with the killing and still Search.
Also if you are lucky enough to find a Torch the Survivor can take two cards instead of one for each search thereby improving the likelihood of finding decent weapons. The issue is that the Torch takes up one of your two equipment options when you really want to have a weapon in each hand.
There are two Survivors that seem to be tailored for Searching. Both start with a free Search action and have the option to hold a torch as their third piece of equipment. So ideal for what is needed. I give you James and Lord Arnaud.
A quick comparison reveals distinctly different characters for later in the game.
James has the option of +1 max Range or Spellcaster for his orange upgrade and then has two combat abilities or Spellbook for the Red upgrade. I suppose that this makes him a Magician as the Range and Combat upgrades are not exactly complimentary. But not particularly potent.
Arnaud on the other hand has +1 die Melee or +1 free Move Action and this is supported by +1 free Combat Action, Iron Hide or Reaper Combat. I think this gives a good range of choices depending on what the game needs. It is easy to see his Melee potential but if the game requires a little more movement then that option is present. When in the red phase you might also need Iron Hide just to survive another turn. I like the balance of options so Arnaud is in!