A couple of things to be aware of, DD is compared to Diablo allot and that is sorta correct but not entirely. A barbarian could fight well but didn't use a bow or magic well, mages could use magic but couldn't fight well etc.
In DD,
any character can become a powerful warrior, thief or mage. All skills are available to you regardless of the character class you start out with, one of the great things about DD. Early in the game you should be adding points to strength and dexterity, especially in the catacombs. I usually use one weapon and one magic with additional weapon and magic skills added as the game progresses. I like the sword early on, one with zero recuperation time. An axe does more damage but you land fewer blows. I usually start out with lightning since it is a ranged magic that works well on Orcs and skeletons. In short, it doesn't matter what class you start with . . . you can build them to be anything regardless of class. I usually start out with a warrior not because I want to be a fighter but because I like his special skill. It can be used while invisible to inflict damage without becoming visible (unless you accidently left click). The mage gets the best start advantage but any class can quickly equal the starting mage skill / ability level.
Also different is the game play, in Diablo you could wade into a group of bad guys, wipe them out, move to the next. In DD you need to slow your game play, use some tactics like luring one or two critters away from the pack, do them in, lure a couple more etc. As you become stronger and put points in the skills you like, you can be more aggressive but . . . you need to think before attacking . . . can I defeat this many Orcs??? . . . depending on the weapons, magic and level you can. The catacombs are basically a tutorial for the game. You don't need to kill every critter and you can come back. I suggest clearing it if you can just to gain experience and levels. I like the combo of sword and lightning but you will find the combo you like and use weapon / magic or magic/ weapon as your preferred combo. Try the magic that you think you will like, max out the one that works best for you.
Also in Diablo, you are grinding constantly looking for weapons and armor. You need to do the same but you will find great weapons and armor more often. The Singing Sword and Sword of Chaos are available mid-way thru the game and I use either for the rest of the game. Same with armor, carefully look at what you find as you can build a very defensive armor collection by mid-game. This allows you to pay more attention to the story and quests IMHO.
Take a look at the starting character skills (see attached image) and you will see there is not much difference with all characters being able to max out many different kinds of character builds with each weighted more to magic, fighting, thieving or any combo of the three.
Hope this helps . . . =)