I'm fairly sure I managed to stun and capture a bloodspider in the last game I finished, using the same methods as any other alien, just more of the same - lots of flashbombs, double-charged stunrods.
I always run the full eight troops, usually two snipers, one machinegunner, one grenade launcher, one SMG close-assault specialist, the last three rifles. I tend to use the Bolter as soon as I can, rarely the laser or plasma rifles. Bolters hit harder than lasers, and I like the fact that you can just buy ammo, unlike the plasma rifles.
Later in the game I'll often equip one "sniper" with a Heavy Laser, and as my teams get better I'll often drop the sniper rifles entirely in favour of more bolters, which has that awesome dual-mode, plus the triple-shot for close work. Machine gun and grenade launcher often stay right through the game, because none of the more advanced weapons quite do what they do.
Plasma pistol for backup weapons on the GL & MG troops, but I stick with SMG for my close-up guy until the particle beam pistol is available; the plasma pistol's magazine is too small for routine use! (it seems to be the only weapon in the game you can fire dry in one round...) I'm also all about the range, I like nearly everyone to be able to "reach out and touch someone", so the plasma weapons just don't cut it, nor do shotguns/flamethrowers/etc - although I do keep those around for base defense loadouts.
Standard nominal field team is MG + one sniper as a long-range engagement team, and two "assault" teams of three, one built around the GL trooper and the other around the SMG/close specialist. All very nominal, of course, as with eight bodies there's never enough to go around...
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