Skaven IMHO is a good match up for us. Yes you will be out numbered but close to half of the models will be skaven slaves, which die just as fast as a lizardmen skink...... Any unit that is considered a hammer (necro knights, both sphinx's, Tomb Guard, Ushabti, colossus, etc) will kill skaven by the plenty if they hit their flank (with a frontal charge from a nice big unit of skellies with a prince on board of course).
The main thing you have to watch when playing against Skaven is their hammers and shooting. Warp Lightning Cannons are about as nasty as war machines get in the whole game and these need to be dealt with IMMEDIATELY!!! After that their hammers consist of the Hell Pit Abomination, Doomwheel (which also shoots), Stormvermin w/Screaming Bell and Plague Monks w/Furnace. Usually a Skaven army will bring atleast 2 of any combination of these and these are your targets for shooting/offensive magic. As for war of attrition, a Unit of 50 Sword & Board Skellies with alteast a Heavily Armoured Prince (I'd also find room for a naked Necrotect if you can spare the points) will beat clan rats and slaves hands down, and will tie up any of their hammer units until you can get one of your own in there for support. Beware of Gutter runners, they will make a mess of your backfield pretty quickly (think of SSC and casket) and are good at assassinating magic casters.
Knowing what lists you usually take would help in deciding what is best for you but as a general starter I would avoid chariots, Stalkers, Swarms and heavy ponies. a Necrosphinx is a must to take out the HPA and some nice big blocks of skellie warriors would be a good start. Add a couple of hammers of your own and you should be set.