Go to megaton and ask for the super duper market quest from the shopkeeper at The Craterside Supply.
Go to the location indicated on your map. Kill everyone inside and grab all the loot. You should find a shotgun somewhere around there.
You might get ambushed at the store. The people outside might have a shotgun.
After you have a shotgun, kill super mutants. Take their hunting rifle.
Congratulations, you now have the two weapons I completed a bit over half the game with. Make sure to grab all the sniping related perks for your hunting rifle.
Lincoln's rifle is the Museum of Natural History. It's full of ghouls, and there's a lot of super mutants between where you are now and there. The alien blaster is out somewhere, consult the wiki. There is a limited supply of ammo and you'll need energy weapon skill. (You already did this)