Aquahog beat me to it, but I already had this typed
, so:
The weapon teams- the warpfire throwersm globes, etc.- come with the Clanrat units. They have no rules- they're just there to look interesting (like the Squig Hoppers and Fanatics in goblin units). You can put them in any units you want, though too few in the clanrats and you can end up with odd gaps.
Clanrats vs Stormvermin is just armour. Every Stormvermin has heavy armour, only two Clanrat do (the champions). Clanrats tend to be naked or have a few rags.
Gutter Runners have capes IIRC, which is unique to them. They also only have swords and other short weapons- nearly all Clanrats and Stormvermin have spears/halberds.
One thing that may confuse you- skaven have a lot of 'command' models. In my own units, all clanrats have two standard bearers per unit, and they also come with two champions (though the command models can fit well with the basic stormvermin if you don't want to use too many champions).
If there are any stands you're still confused about I recommend posting photos.