Depends on how much warmachine spam he engages in, but generally speaking;
Slann with Light gives you some gun-magic to soften up his hordes, 'Net' for slowing Rat Ogres (the only close-combat problem aside from the Hell Pit you'll face), 'Pha's Protection' to shut down his warmachines, and of course the combat buffs to make your Saurus go first. Shadow is also a good Lore, and of course Life because 'Dwellers' will remove entire blocks at will.
Old-Blood will chew through most of their characters with no problem, so he's kinda overkill. Scar-Vets will probably be enough. Sword of the Hornet/Swift Slaying is an excellent choice, as it solves your low Initiative
EOTG makes Skaven cry, because it hands out ward saves against their warmachine fire, and once they reach your battleline you can switch to 'Burning Alignment' and rack up the kills. 'Blizzard' from the Priest on top is also useful for shutting down a warmachine. Of course, if you roll 'Chain Lightning' or 'Comet', you'll also be killing stuff.
Saurus need to be buffed, as static combat rez will be against them and you're gonna take a lot of S3 before you get to strike (Skaven specialise in outnumbering every army ever with just their Core blocks). Light magic helps here, but once you have 'Speed of Light' or 'Timewarp' up (or both haha), you'll demolish even Stormvermin.
Skinks with blowpipes are a pretty good way of eliminating weapon teams and warmachine crews, as per usual. Just be sure to blow away the attached unit of the weapon team first with magic or Salamanders, as if you don't, they get a 4+ ward (which might let them survive your hail of darts).
Stegs are good as counter-chargers, just be aware that warp cannons, warpfire throwers and his magic can all obliterate them. So, hide inside the Gungan shield, and flank charge stuff that tries to engage the Saurus battleline.
Camo Skinks obviously as good, but extremely suicidal as per usual.
Temple Guard will outfight most things, Rat Ogres will rip them up but ultimately succumb, and if you buff them with Light magic or nerf enemy Initiative to 1 with 'Miasma' from Shadow, you'll cut them down before they can swing.
Salamanders are, as per usual, worth their weight in gold. Skaven in particular hate Leadership tests (even in BSB range, they're usually taking them on an 8), and nothing in their army is heavily armoured or especially tough (except Rat Ogres). If you snipe out the BSB early with Blood Statuette or magic, Salamanders will route his entire army after two turns uninterrupted fire. And, if he wastes warmachines, magic or Rat Ogres trying to kill them, thats more Saurus or Stegs not taking wounds.