Beam Shooter Mod is costly, but pretty usable (a bit moreso than its non-mod counterpart for that cost). Blast Magnet Gun Mod... I've no experience but the ammo seems pretty low.
Blast Railgun is usable. It has a low projectile speed and I think bothersome charge time compared to normal railguns, but it has enough ammo to be pretty comfortable to detune and not worry about running out of ammo. It's probably better to toss it on an S-Art since M/L have access to the much handier Linear Cannon. You'll need +10% speed to compete against a base Railgun/Linear, and +20% to compete against Saggitary Maxis. After deciding on that, you can probably dump Force on the remaining 1-2 slots.
Most people will say Burst Missile AMJ. It is the cheaper of the two to fit on a bot on both counts (80 end cost and only 50 net capacity consumed, compared to 120 end cost and 80 net capacity consumed). Burst Missile fires missiles that split into three, Comet Launcher is kinda like a rapid-fire version of Toybox's Napalm Missile AMs. Burst Missile has better force. Honestly, though, while I also recommend Burst Missile, I also suggest that you try putting both on when you get her, and just seeing how you feel about each. See which one works better for you, not what works better on paper.
I haven't noticed such an increase myself, at least nothing different from the last several weeks. Mialies have been in a sharp numbers increase for a while. The other three I haven't seen much rate change, nor any particular changes that would've led to an increase other than just follow-the-leader of some individual(s) who simply decided to start using theirs.
