Once you hit level 15 - about right after you complete Roseway - you can start Murder on Eridanos DLC. Entering combat armed with your tier 1 - 2 stuff can prove challenging, though, namely of you play on higher difficulties. Fortunately you can pick up (steal in most cases, to be exact) some tier 3 weapons on Eridanos before you get yourself into trouble. In this short guide I will describe where you can get it.

The most important thing about your weapon is its level, then the mods you added. Do not bother to hoard uniques - levelling them is costly and the best you can do with them is to sell them once you outgrow them. The only weapons that are really worth upgrading more than some 5 levels are so called science weapons, once you have high enough science skill to cap the upgrade cost per level. Pristine is nice to have, but do not expect the maintenance hell you remember from FNV in this game. If you check your gear from time to time, you are good.
So in principle what you want is to get a high level (normal) weapon - the higher the better - mod it and live happily ever after.
Which is exactly what happens if you enter Eridanos as early as possible. Note, though, that using the high level - tier 3 - weapons elsewhere literally breaks the game. Simply put, you will oneshot everything no matter what weapon you use, and only the boss mobs will need to be shot twice.

Once you leave ship, run around the landing pad and loot everything you can. Your first tier 3 weapon is a spacer's choice pistol on a crate around the tail of your ship.

The entrance to the spaceport itself will be very likely blocked, as you need to advance in the main quest before you can get in.

Fortunately you do not need to enter to loot your first tier 3 light assault rifle, as it is in a booth just before the closed gate. Just make sure (as always, you know the drill, you thief) the SLUG guardsman that hangs around does not see you.

Travel north to the closed gate to Wilderness Exploitation Reserve pad. The guard booth you are going to loot here is locked; you can however climb to its roof using a ladder to the north and drop down inside through a vent hole.

Once inside, you can steal a deadeye rifle. Now I know you are all grown up but sorry you WILL have to play the mighty sniper from time to time at least until you level up a little, so stop complaining and grab that gun, you will need it. Thank me later. You can open the door from the inside, a switch is to the left.

Travel southwest and look for an add stand next to the pool.

The tossball stick you can pick up there can get handy (don't be selfish, you companions need some good stuff, too), and you even do not have to steal it, free for taking...

The time of innocence is over, you will have to fight for this loot. Once you talk to Lou for the first time (right after inspecting the crime scene), and he unlocks the gate to Orchards for you, make sure you loot the small isle in between the hotel plaza and Orchard (the position arrow is not easy to see on the screenshot as usual, look for the workbench sign).

If you have problems, consider setting your companions on Defensive and headshot all of the canids you can without being detected, then, once the survivors finally realize where you are, use your companions special attacks to finish it. Both SAM and Parvatti works nice.
Once it is safe to explore and loot, climb down a ladder on the southwestern side of the platform where you arrived and right behind a corner - not far from the spot where you saw the first canid - is a workbench with a plasma rifle and a bolter pistol on the ground next to it.

Another bolter pistol is next to a dead SLUG security, and you can also find an unique Frigidariator[theouterworlds.wiki.fextralife.com] in a small cave to the north, together with some ammo.

You already know; but if not, just start the quest I'll Not Ask for Guests[theouterworlds.wiki.fextralife.com] once you enter the Wilderness Exploitation Reserve, and loot the pistol from one of the bodies you encounter along the way.