Your loadout should be pretty good here:
1. Polaris - Elemental Damage
2. Biohazard - Shadow Damage
3. Snarble Barb OR Spine Cone - Piercing
It's good that you chose the piercing sword or bomb as it is often recommended to use the piercing damage on Tier 3 beasts and fiends rather than piercing guns. Your fourth weapon can be a status bomb like Ash of Agni or Shivermist... or even the tried and tested Calibur swords.
For your low levels, get a magic hood and owlite for your first 2* equips so you can head over to Ironclaw to farm tokens. As for initial ICMF-running choice, I'd go with Calibur or Blazebrand for a sword, + your choice of non-shock bomb or elemental alchemer of your choice that is not voltech.
In order for your gear to be viable, you need to always have a sword available that you can use against any mobs where swords are useful. A normal damage sword such as leviathan blade lets you do this with a single sword. Alternatively, you could get two swords of different types, such as getting the barbarous thorn blade that you're planning on, and also getting a glacius. That way, if you're fighting mobs where one sword doesn't work well, then you can switch to the other.
You need the same for guns, and for bombs. You need all three weapon types in order for your build to be viable. For what it's worth, I'm not impressed by the spine cone line. The mobs that you most commonly need to use bombs against are slimes and constructs, and both are highly resistance to piercing damage. You can get a dark briar barrage and also some other bomb, but you'll have to use the other bomb most of the time.
You should also note that, even in situations where you need a gun and elemental damage is viable, sometimes a pulsar isn't. The large graphical explosions cover up mobs, so that you can't see if they're attacking or not. More to the point, your teammates who might be trying to melee those mobs can't see if they're attacking. That means that to attack the mob is suicidal for them. If they're forced to back off, then that means that your pulsar does negative net damage, once you subtract off what your teammates would have done if you had let them attack. Alternatively, if they attack anyway, then that means that you're killing your teammates, and thus doing more harm than good.
Now, that only applies in some situations, of course. If every pulsar attack interrupts the mob, as with gun puppies, then you can spam away and the explosions ensure that the mob is not attacking. If you're attacking something that no one else on your team should be attacking, such as if you're solo, then you can likewise spam pulsar. But it's a tricky gun to use properly, and most people who use it manage to do more harm than good with it.
You also need armors. You need something to defend against each of piercing damage, elemental damage, shadow damage, shock condition, fire condition, and freeze condition. The same armor set can sometimes work for two or three of those, so you don't need six separate armor sets. But you'll need at least two or three.
You need all of that for shields, too, as well as something to defend against the poison condition. Getting poisoned isn't so bad, but having poison attacks break your shield and leave you vulnerable to other attacks is a problem.
Note that four star gear is viable all the way to the core. A good variety of four star gear is more effective than one set of five star gear that you're forced to use everywhere. You do want to eventually upgrade to five star gear, but it's more important to get a good variety of four star gear first.