I played at least decent amount of time with every weapon with no favorites. And I want to say EVERY BH's ranged weapon is viable and usable. You just execute them a little bit different from weapon to weapon. For example: most likely you cannot one-shot Chaos Warrior with pistols (pistols does not penetrate armor) but pistols has mentionable sustain potential or you want to hold trash mobs in line in front you while holding volley crossbow in your hands, with repeater pistol you want them to come a little closer.

Side-Arms
Pistols has an utility. No reload, quick "run and gun" mechanics, good headshot dmg. But in case of pistols I want to mention that you have to change your talent tree. About this scroll a bit (but better keep reading).
Volley crossbow. Long reload, in most cases after alt-fire you want to "reload" it by resetting your passive skill (on melee kill) rather than shoot several times and do "fulltime reload". Has great dmg if you hit all of 3 arrows in alt-fire. Almost no dmg reduction for far distances.
Repeater pistol. Quick reload. Great burst fire in alt-fire mode. Normal LMB shots provides you with mobility to react. E.g.: lich behind your back, assassin rat's jumps, another "jump scares". You can shoot alt-fire with this gun for about 20 meter away with minor damage reduction. So yea, not necessary to come/wait for face-to-face.
Crossbow. Great one arrow dmg and penetration. Likely to one-shot specials on far distances. One-shot Chaos Warrior in the head on closer distances. Very popular choices are Volley Crossbow and Repeater Pistol.

Melee
Melees pros and cons are more obvious than side-arm's. First of all, want to point out cold weapons I don't like:

Two-handed long-sword. Someone may argue like "It has much stamina, great cleave etc". But I really dislike this weapon. You get no additional dmg to compensate it's slow swings and cleave isn't good enough to overshadow falchion's cleave. I won't recommend to start your BH progress with this weapon.
Rapier. Has a special weapon action a.k.a "water pistol". "Water pistol" provides with good utility (you have no ammo? But you have rapier special), decent close range dmg and some crowd control. I do really like rapier's attack speed and clear trash mobs potential. But apart from it has nothing. Even overpowered BH sometimes cannot one-shot trash rat. What to say about Chaos specials. You have to prepare heavy headshot attack so your dmg be smh mentionable. TL;DR: great trash mobs clear, the worst in everything else.

Important note I want to mention: Axe, Flail and Falchion has an equal usability. I can't say one of them is super better or super worse. Every one of them excels in different situations.

Axe. Deal halved dmg to shields, penetrates armor, decent cleave, decent attack speed. Well rounded weapon.
Flail. Completely ignore shields (direct body dmg), has no armor penetration, low stamina (two points), good attack speed, below average cleave compensates with better attack speed.
Falchion. Probably the best cleave, good attack speed, penetrates armor, two stamina, good headshot dmg.

How do you choose:

Want cleave, penetration and good attack speed? Falchion.
Want be at easy when you face shields, has enough stamina to defend yourself and armor penetration? Axe.
Want to give 0 f about shields, satisfy yourself with juicy headshots, and have enough ability to clear trash? Flail.

These three above are really good well rounded weapons in this game. Along the way I just switched between them when I received more powerful kind.