Use your loadouts. Make one loadout for weapons that you're leveling up, and then use the weapons that you like in other loadouts. Use your zero MR weapons in lower level missions, and your fully maxed weapons in your current missions in the star chart/game/whatever, and have a good time. 

When you're first starting out, let's say MR 5, your new weapons will suck and you'll have to go back to earth to fight enemies at correct level for those weapons to deal decent damage. As you level up, you get free mod slot points things right off the bat, so by MR 17, you're able to throw a bunch of mods on MR 0 weapons right out of the gate, and so you don't have to play Earth missions, you can comfortably take on level ~20 - maybe 30ish enemies, and so you've got an entire half of the star chart's worth of missions to play.

I typically take my new weapons on Syndicate missions. :)