D2 lod yes, hc too. Not d2r. I've done barbarian many times at the beginning. It works. It's just quite different, and you have different things to look out for as opposed to purely ranged, minion or magic based characters.
I've experimented quite a bit .. First off i like to start with spear, the range of the spear makes it easy to deal big damage from a little bit of a distance. As soon as you find a socketed shield and gems, make a resistance shield, and put on switch with a scimitar or quick-swing weapon.
One funny different route to go, is to make a throw barb from the beginning. Use throwing knives and/or axes. Being ranged has some advantages. You're not constantly surrounded by monsters taking damage. Boss fights too, mephisto and diablo becomes easier.
But it all depends on the gear. If you find a good weapon, you should try to build around it. Once i found a gleamscythe early in the game, which i used for a long time. Used concentration and sword mastery with that. Later on, i found an almost perfect bonesnap, continued with concentrate and reskilled to mace mastery. When or if going through places with a lot of elemental damage, switch to the 1h-weapon and shield, less damage, but higher resistances.
I play solo mostly, i don't use shouts until level 24 when battle orders become optional. It may be more relevant if in a group with many melee characters taking many hits, using shout early, to get the defense bonus. But just being in front and dealing damage, killing monsters, is a good contribution in itself. Be the tank in front that others work around.
One last thing that is important to remember. When you run, your defense is set to 0. Meaning, whenever you move, you take 100% hits from monsters. This can be a death trap playing hc. You can press R to set walk/run to walk instead of running, meaning you retain 50% defense. Either way, it is most important to read the scene - meaning, don't engage in a group of monsters you know with close to 100% certainty you (and if they are there, your group) can kill without taking too much damage. If you start taking a lot of damage, and then run away, you may take -more- hits in a quick session, which can be fatal. I.e.; Don't engage if you aren't sure. Furthermore, at least when playing hc, you running away, may mean your team members may be overrun too, if they've come to depend on you tanking damage, they may have low hit points and defense, meaning they can be killed much faster than you. This is the role a barbarian usually plays... the tank that the others work around. And of course using shouts to agument the team.
A well developed team this way, can use the barb to draw monsters, but the barb takes almost no hits because everyone kills the monsters quickly. But the barb still plays that role.