Since all weapons you encounter throughout the game will have detailed statistics on their weapon cards and since weapon acquisition is mostly random, memorizing the characteristics associated with each weapon manufacturer is probably much less important than simply closely studying the stats of each weapon you find to see if it is compatible with your playstyle.
Be that as it may, here's a quick review of the weapon manufacturers in Borderlands 2 including their defining characteristics:
Vladof
The defining characteristics of Vladof weapons is their high fire rate which is particularly noticeable in Vladof snipers and Vladof pistols. Vladof snipers can easily double as long range assault rifles, i.e, holding down the trigger button will produce automatic rifle fire. Vladof pistols have the highest fire rate of any pistols in the game and are essentially machine pistols easily rivalling the steady firepower of SMGs. Vladof is my favorite weapon manufacturer in the game and I highly recommend looking for a Vladof pistol in the first Guns vending machine you encounter in Liar's Berg (Chapter 2, Cleaning Up the Berg) and throughout the game. Look for names like TMP, Anarchist and Troublemaker. These are all Vladof pistols.
Note that there are no Vladof shotguns or SMGs.
Torgue
Torgue weapons specialize in dishing out explosive damage and the best Torgue weapons, in my humble opinion, are either assault rifles or shotguns. Explosive damage bullets have a blast radius meaning you don't have to be right on target to do damage to the enemy which is particularly useful against fast-moving skitterish enemy types like Varkids or Rats. Torgue shotguns are excellent PWR Loader busters since PWR Loaders (robots with spinning blades for arms) will deflect all standard ammo back at you.
Note that there are no Torgue sniper rifles or SMGs.
Jakobs
Jakobs weapons are noted for their high damage but also have high recoil. This means that the muzzle of your gun will rise much higher than most after firing which may put off your aim for any shots that follow unless you adjust. The first sniper rifle you earn as a a mission reward for completing an early side mission, Bad Hair Day, is highly likely to be a Jakobs. Jakobs snipers don't handle nearly as well as Vladofs and have a much lower fire rate but they do dish out heavy damage. Look for names like Chinook, Muckamuck and Tumtum for high damage snipers.
As for other weapon types, another defining characteristic of Jakobs weaponry is that they are all semi-automatic although they are touted to fire as fast as you can pull the trigger rendering Jakobs Fire Rate statistics completely moot. An annoying characteristic with Jakobs shotguns is their small magazine sizes so firing as fast as you can pull the trigger is pointless if, say, you've only got two shots in the magazine. Also, for PC gamers, having to rapidly mash on the fire button (typically the left mouse button) to take full advantage of the 'fire as fast as you can' feature for Jakobs assault rifles or revolvers may throw off your aim unless you can manage to hold your mouse rock steady as you mash.
Note that Jakobs weapons have no elemental damage and there are no Jakobs rocket launchers or SMGs.
Dahl
Another in the line of weapon manufacturers specializing in cool-features-with-a-catch is Dahl whose defining characteristic is burst fire while zoomed. Dahl weapons will typically fire from two to six bullets per pull of the trigger when they are scoped or aimed down the iron sights. This is very useful for sniper rifles but in my humble opinion pretty much useless in all other weapon types since automatic fire is much better than burst fire while zoomed.
An example of Dahl weaponry is found in the first weapon you acquire in the game to complete the My First Gun mission. The repeater you get from the cabinet in Claptrap's Place is always a Dahl repeater. Aim down the sights while firing to make it fire two shots per trigger pull.
In sniper rifles, look for ones with 'Scout' in the name. These are always Dahls and are very useful for enemies that can't be one-shot. Dahl snipers with elemental effects are extremely useful for affected enemy types, e.g., corrosive Dahl snipers make short work of Loaders, shock Dahl snipers can wipe out Stalkers' shields and take them out of stealth mode with a single pull of the trigger. Dahl snipers with Slag properties are extremely useful since a 3-round burst fire (which is typical for Dahl snipers) coupled with a chance to slag over 35% means a guaranteed slag for every pull of the trigger.
Note that there are no Dahl rocket launchers or shotguns.
Hyperion
Hyperion weapons specialize in increased accuracy while firing meaning the more you fire the weapon, the more accurate it becomes. You can think of 'accuracy' as an imaginary cone that spreads out from the muzzle of your gun. The tighter that cone, the more accurate your gun fires. Hence, Hyperion weapons will tend to spray all over the countryside for the first few shots after which their aim tightens up to pinpoint precision.
Hyperion weapons will also sway wildly in your grip for the first few shots after which they stabilize dramatically. This is especially noticeable in sniper rifles in which you essentially have to take a couple of shots to get the rifle to 'calm down'. After this the sniper will hold rock steady and fire dead accurate. This is useful for snipers who like to remain scoped until the magazine runs dry and then reload. On other hand if you like to jump in and out of scoping your rifle to displace or acquire another target, Hyperion snipers will be annoying at best. This also means that Hyperion snipers are useless combined with the One Shot One Kill skill which requires you to reload after every shot to take advantage of bonus damage. On the other hand, Hyperion snipers will excel with the Kill Confirmed skill which gives bonus damage for remaining scoped.
Other good Hyperion weapons are shotguns and pistols. All shotguns typically have low accuracy so Hyperion brand shotguns benefit greatly from an accuracy bonus from being repeatedly fired. Hyperion pistols can also be coaxed into firing with absolute pinpoint accuracy after taking just a few shots. On the other hand —and contrary to the info in the official game guide— I found Hyperion SMGs to be ridiculously inaccurate until you emptied out a good half of the magazine leaving you with less than a dozen shots of accurate automatic fire until you're required to reload (and reset the Hyperion accuracy stabilizer).
Note that there are no Hyperion rocket launchers or assault rifles.
Maliwan
Maliwan weaponry specializes in elemental damage and this is what you'll be looking for early in the game until all weapon brands except Jakobs and Torgue have a chance to have elemental properties. Note that Torgue weapons are excluded because they're always fitted with explosive damage (see above).
Other non-Maliwan-Jakobs-Torgue weaponry will start getting randomly fitted with fire damage starting at character level 7, with shock damage at character level 11, with corrosive damage at level 13 and slag damage at level 15.
Maliwan SMGs are the best since their automatic fire abilities coupled with a high fire rate and good magazine sizes means a guaranteed elemental effect before the magazine runs dry.
Note that there are no Maliwan assault rifles or shotguns.
Tediore
Tediore weapons sport the ridiculous ability to explode like a grenade when reloaded. This means that every time you reload a Tediore, your character will toss the weapon away at which point the tossed weapon will explode with a force commensurate with the amount of ammo remaining in the magazine when the weapon was reloaded. Some like this feature but I personally thought it was insane and utterly useless since a veteran gamer like myself has become very accustomed to reloading on the fly, i.e., while taking cover or running away. Using Tediore weapons requires you to adopt an entirely new reload discipline where you have to now take aim at a viable target before reloading. It's either that or waste the grenade option and/or risk blowing half your face off should you be reloading while taking cover with, say, a Tediore rocket launcher.
And for this reason, I always immediately sold all Tediore weapons I acquired.
Note that there are no Tediore assault rifles or sniper rifles.
Bandit
Bandit weapons with their kooky designs and mediocre stats all share one special feature and that is they have large magazines. This is excellent for protracted firefights when cover is scarce and having to frequently stop to reload your weapon is not desirable. However, the bottom line is, once progress into the game, you'll encounter so many other weapons with a much better assortment of bells and whistles that having a large magazine won't seem like that much of a big deal in comparison. Notwithstanding, Bandit brand pistols can be very useful early in the game when good weaponry is hard to come by. Later in the game, you should definitely consider doing the Note For Self Person mission (see the video at the top of the page) to get your hands on a great Bandit brand unique rocket launcher which will serve you well throughout the rest of the game (good Saturn Buster).
Note that there are no Bandit sniper rifles.