Honestly, I'd be inclined to go with no support weapons at all. Use their mobility to the fullest, and equip them with something high on damage and low on range. If mechs are motivated to avoid a jump platoon's engagement range and have a chance of doing so, you can use those platoons to influence the movement of those mechs, herding them according to your designs.
If it'll get you another point or so of damage, I guess go ahead and give them a support weapon per squad. Above all, do not slow them down. The Auto Grenade Launcher might be good here. Anything with a crew value of 1 (not 1E) is good, as well as a base range of 1 through 4. That's how you get the -2 modifier at pointblank range that convinces a mech or tank that they wandered into the wrong neighborhood. (Note that the light machine gun Challenger mentioned fills this requirement, but none of the heavier ones do, nor do any kind of support laser.)