qaqc,
With a 120V MIG machine, he -WILL- be doing short-circuit transfer. That machine doesn't have the voltage to get into spray transfer on steel. Not that spray is needed to do gauge or 1/8 inch material.
Filler metal is filler metal, but (there's always a but somewhere) the diameter of the wire used in GMAW/FCAW/etc does limit both min and max amps that can be used.
That said, for GMAW on mild steel, any argon-CO2 gas mix from C-25 to C-8 will be fine for short-circuit transfer with that little machine. Plain CO2 will also be just fine as well, much less expensive that C-25/etc, and the down-side is a little more spatter (than C-25) and a bit hotter arc/more penetration making things a bit more difficult on thin gauge steel sheets.
0.023/0.025 versus 0.030 wire? The difference is usually about 1 gauge-size capability difference on the high and low ends. So that's 24 gauge low-end for 0.025 wire versus 22 gauge low-end for 0.030 wire. Your call.
Most of this is in your manual and also on the nice door chart that Lincoln puts on the door to the wire compartment. At least for mild steel parameters.
Lincoln L-56 is an ER70S-6 wire, as said. If you need or want the 'extra' deoxidizers in an S-6 wire, it is just fine. If you have clean steel with no mill-scale, you could use an S-3 or S-4 wire, which have lower deoxidizer levels than the S-6 wire. About the only drawback to using S-6 wire when an S-3 or S-4 could have been used is that you get a little bit more silicon islands (those little 'glassy' usually brown glossy drops) on top of the weld bead when you are done.
L-56 is just fine in my book.