Constructing from blueprints just automatically creates a pre-set gun for you from your available weapon parts and resources. If you don't have the weapon parts or resources that a blueprint needs, you still won't be able to construct the gun from a blueprint, like if you're constructing a gun manually. I don't think it allows for a "cheaper" gun.
It's a good way of experimenting on what gun parts do and what kinds of guns you can build, though. Also, if you prefer the classic Dead Space 1 and 2 guns, you can just easily build them from blueprints. Like manually constructed guns, guns constructed from blueprints can be dismantled (so you get the parts back), and modified, if you like the gun you got and would like to improve/tweak it a bit.
If you want more control over your resources, avoid creating weapons from blueprints, as it will automatically create a weapon part from your resources if a blueprint requires a part that you currently don't have. You might want to just look up what parts make up a blueprint at a Dead Space wiki site, instead. From the Dead Space Wiki's "Dead Space 3 Weapons" article:
Blueprints do the assembly work for you, but do not add anything you can't make using the manual assembly interface. A blueprint will use any matching parts that you already have before producing new parts using resources. If you have some parts, but not all, it will use the parts you have and then use resources to make the rest. Parts already being used by weapons in your safe will not be used, so if you want to use those you should either disassemble those weapons first or just modify the weapon manually.
An advantage of collecting blueprints is (From the IGN Dead Space 3 wiki, "Blueprints" article):
Once the player finds all the blue prints they will get special Upgrade Circuits. These Upgrade Circuits include:
+3 Fire Rate, +2 Damage
+3 Reload, +3 Clip