There are 2 sets of passwords in the office with no weapon lockboxes to be found. There is still a room that can only be opened with a Lockpick, but there is no other way to access that room. Both of these codes are required for progress.

Code: 24681
Panel: You pass the panel on your way to reach the book. It is marked on the map here.
Book: On the floor of the far bathroom
Code: 999912
Panel: Once again, you pass it on your way to the book.
Book: On the ground near the Gold Key

There is only 1 code on Urban, which is on a weapon lockbox. Progress on this level is gated by using key items.

This is the best level for grinding characters due to the combination of panels, enemies, and level brevity. You get EXP for every puzzle you complete, even the ones requiring key items like the Toolbox. Once you are familiar with the level you can knock it out in about 20 minutes on single player or 12 minutes with at least one partner in multiplayer. As you get higher in level, gradually increase the difficulty to maintain efficiency.

Code: 1426
Box: At the end of the alley, south of first toolbox panel
Reward: Magnum

Codes on this level are required for both a weapon lockbox as well as key items required to progress. The majority of the codes are found on various gravestones with different books telling you to look for different names. I will not show you where to find the different graves, but I will give you all of the codes.

Code: 872311
Box: By the dock
Source: There are 3 statues near the exit where they have partial combinations etched into them
Reward: Blowtorch

Code: 1911
Box: On the main road near the exit
Source: Date on Mason's grave
Reward: Magnum

Code: 1892
Box: Near the crypt
Source: First two digits on Vernon's death year with the last two digits of Morgan's death year
Reward: Toolbox

Similar to Urban, this level only has 1 code, which is used for a weapon lockbox. This level has the fewest number of key items needed to progress.

Code: 1944
Box: At the end of a burning hallway near the beginning/end of the level
Source: Flier (book) you'll find near the midpoint of the level
Reward: Magnum

This level only has a single code that is required to progress. Due to the code input being near the beginning of the level, I recommend entering it immediately before tackling the level in full. This level changes things up on us a bit by having us interact with terminals to both find and input the codes.

Code: 112358
Terminal: Near the start of the level, glowing, can't miss it
Source: Terminal in Eastern Maintenance

Before we get started, I have to preface this with that in every optimal build, you are not going to be starting with any special weapons in single player. You only have 16 skill points to play with, and all of them are WAY too expensive for what little benefit they offer. When playing multiplayer, there are some gimmick strategies where you can start with something, which you are going to give to someone else who actually has the damage buffs. As you play the harder difficulties, you need to kill everything else before they kill you, making anything other than damage boosts sub-optimal.

Lydia
Lydia is the handgun specialist of the game and one of the recommended starting characters. She can turn the most plentiful ammo in the game into a serious threat and is my preferred character. Combine her level ups with both Marksman and Soldier, and her pistol shots will do over 40% bonus damage. She will do the heavy lifting in most of the levels and can even fight bosses with her handgun. I rate her as one of the two best characters in the game.
Perks:
0.5% firearm damage per level, 12.5% max
0.25% handgun damage per level, 6.25% max
0.5% damage resistance per level, 12.5% max
Starts with unique Handgun

Build: The optimal build on Lydia is going to be combining Marksman and Soldier for a 25% damage boost to all of your gun attacks, not just handgun. This means anything she shoots other than the Grenade Launcher will get a 37.5% boost at max level. Backpack may look tempting, but it is too expensive, forcing you to sacrifice Marksman. The damage resistance and health boosts are actually weaker as you progress through the game and completely worthless on Nightmare mode, so I recommend skipping them entirely.

Kane
Kane is the original melee specialist in the game, and a bit of a trickster character than anything. This is because while he is most dangerous up close and personal, due to the fact he takes increased damage almost negates this bonus. He innately starts with a lockpick, allowing you to bypass all of the weapon box codes. This is not a good thing however as Kane has a penalty when firing anything other than the Grenade Launcher. Despite this contradiction, I rate him as the 4th best character in the game. If you learn how to melee properly, he is one of the strongest damage characters on Nightmare mode, where his fragility is a moot point.
Perks:
0.75% health per level, 18.75% max
1% melee damage per level, 25% max
Starts with a Lockpick and Knife

Build: The optimal build here is going to be melee boost, Fighter and Brawler. These will boost his already impressive melee damage through the roof, to 65%, with a bonus on top of this on Nightmare mode. Do not start with the Fire Axe as the Knife you have anyway is already better. If you are solo, save the Grenade Launcher for the boss when the time comes and knife everything else that gets in your way.

Ivy
Ivy is the tank character of the game, and the one I rate to be the worst character of hte six. You have damage penalties for both melee and guns. At higher levels, your shotgun will be a little bit better, but you'll only have that and the Grenade Launcher to fall back on as weapons. Since ammo for neither of those are common, she is left in an awkward spot. To make things worse, she still dies in one hit on Nightmare mode, meaning she has literally nothing going for her when you play the harder difficulties. She can support a team on multiplayer, but there are just better options.
Perks:
0.7% health per level, 17.5% max
0.4% shotgun damage per level, 10% max (this is actually a net 2% due to her debuff)
0.65% damage resistance per level, 16.25% max
Starts with Painkillers

Build: Lucky is probably her best skill since it can give you bonus ammo, allowing you to get a little more out of Grenade Launcher and Shotgun ammo drops. You could start with a Shotgun to get your primary weapon and a little extra ammo for it, and due to lack of superior options, this may be the way to go on her.

Harry
Harry is the best all around character in the game, competing against Lydia for the top spot. He has a Backpack innately, allowing him to carry more items. His skills on level up are all great, and he has access to some of the best skills in the game. Despite this, he cannot compete against Lydia's handgun, but he can use literally anything else. He can even tie Kane in regards to melee performance. This is the best character to play on single player and someone who can fit into any composition on multiplayer. His penalties may seem bad, but they are completely nullified on Nightmare.
Perks:
0.5% firearm damage per level, 12.5% max
0.5% rifle damage per level, 12.5% max
0.5% grenade damage per level, 12.5% max
0.4% magnum damage per level, 10% max
1% melee damage per level, 25% max
Starts with a Backpack and Fire Axe

Build: Harry has flexibility in his build. If you want to use guns, go Soldier and Marksman, and you get a 40% boost. If you want to melee, go Fighter and Brawler for 40%. If you want to support a team, go Lucky. You even have Boom if you want stronger Grenades. Harry is the most versatile character in the game, so make sure to take advantage of that.

Hank
Hank is the first of the characters here who actually has some drawback to the benefits he gets. Despite this, I still rate him as the third best character in the game. The main issue here is that he does not have access to the strongest skills in the game, which means he isn't as strong as the other characters at max level. Despite this, due to his critical modifier, he can still pack a nasty, but inconsistent punch.
Perks:
0.5% shotgun damage per level, 12.5% max
0.5% rifle damage per level, 12.5% max
0.5% grenade damage per level, 12.5% max
0.2% critical hit chance per level, 5% max
Starts with a Shotgun

Build: You can choose between the melee and firearm boosts, but without the tier 3 ones, you're a little limited. As such, you can opt to take defensive bonuses for the lower difficulties, but these are a waste of points on the higher ones. I would recommend going for the tier 1 melee and firearm boosts while starting with the knife, which makes you a little more rounded for whatever you encounter. Only take the tier 2 skills if you know you can specialize as they bring penalties with them.

Elena
Elena is similar to Kane, but she lacks the highest tier of melee skill, which is why I rate her 5th of the six. Luckily, she is a better support in multiplayer should your allies claim Lydia, Harry, and Hank than Kane while not being as bad as Ivy. Due to her critical chance penalty, her firearms are a little less reliable than the other characters (except Ivy), but the good news is that she does have Lucky. She also has Marksman, so she can use guns, just not as good as the previously mentioned three. Additionally, her innate poison immunity is worthless on Nightmare, as is her health per level.
Perks:
0.5% health per level, 12.5% max
0.5% handgun damage, 12.5% max
1% melee damage per level, 25% max
Poison immune

Build: Elena lacks the tier 2 firearm skill (Soldier) and tier 3 melee skill, making her specs a little awkward. On solo or small team play, you can go Marksman and Gunner for some bonus firearm damage, turning her into a poor man's Lydia with a crit penalty. On larger team play, I recommend Lucky with melee skills.