Hoooooold up!!! I have 6000-6500 points of skaven so I can give you some pointers here.
First I'd like to point out its army books in fantasy no codex's here

haha
Anyways basically it depends on your area what points levels you play. With my friends at home I play 2k or 2.5k (2.5k at the
flgs)
Basic things you want:
Slaves - units of 40-50 with a 5 wide formation is a great tarpit unit (the best in the game arguably)
Clanrats - usually 25-30 as a bunker unit to hold onto your chieftain battle standard bearer and grey seer (if you have him on foot) equipt with hand weapon and shield everyday all day
Stormvermin - run these about 40 with a storm banner or razor banner and that's a pretty elite type choice for skaven (its not strong tho compared to other armies tougher choices but they are only 7 points each tho)
Plague monks - no armour but running then 35-40 with a plague banner is an awesome unit
Jezzails - not recommended at all they don't hit very often (and the $ of models is outrageous so just model some up with kroot arms on clanrats)
Censer bearers - situational unit but some people like them but they are pricey points wise for what they do
Globadiers - again situational and pricey
Gutter runners - units of 5-9 with slings and poisoned attacks are almost a must take as war machine hunters
Rat ogres - people harp on these a lot but they really aren't that bad. They are a little expensive and have no save but they are unable. If you aren't playing competitive then you'll be fine with running a unit of 6+ and you can boost them up with Skweel but the problem is he only gives them a regen save sometimes (depending what you roll)
Warp lightning cannon - these are excellent for the points cost (best for the points in the game some say) I'd buy 1 to start then get 2
Doomwheel - awesome unit and very fun pick one up for sure
Hellpit abomination - this thing is a beast, its such a good monster just watch out for flaming attacks (he won't get his 4+ regent against those) he has a chance to get back up when he has random movement, random attacks he's great
Screaming bell - some people like them some people don't. I'm not a huge fan but they can be fun its not the best or most competitive option tho
Plague furnace - fun unit cheaper than the screaming bell and is much more offensive. It lacks a save tho (only has magic resistance 2) so watch out for cannons. Gets pushed by 35-40 monks with the plague banner its a scary unit
Warlords - cheap and effective generals I usually equipt them with armour of destiny and a halberd on a war litter and plop him in a unit of stormvermin, pretty cheap and effective
Chieftain - he will be your battle standard bearer, give him a talisman of preservation (or a 5+ ward if you give the seer the talisman of preservation) and halberd and put him in your bunker unit
Grey seer - usually give him the talisman of preservation and some magic items. Common ones include skalm, power scroll, earthing rod etc
Assassins - pretty expensive but you can give one the potion of strength and weeping blade for a nice little punch in your army
Warlock engineers - good cheap wizards. Most common is one without a wizard level and give him a doomrocket...that's the scariest 45 points you can spend (unless you blow yourself up or miss
lol)
Plague priests - these are nice and give you access to the plague lore. I usually only take one to get access to the furnace but when I do give him a flail and a 5+ ward save
Vermin lord - over priced. Still fun sometimes I've used him a few times now
Special characters - meh usually all over priced. Queek is okay if you want to run some stronger stormvermin.
Weapon teams - only worth while ones are the warpfire thrower and the mortar but are super expensive. Some people like the rattling gun (it misfires the least the others misfire like crazy and can be bad
lol)
Giant rats - best chaff unit in the game. A chaff unit is a redirect unit, a unit that blocks charges etc. For 23 points you normally want to run 2-4 of them per list depending on the points level. Use the giant rats included with the plague monks, doomwheels, and hellpit (I haven't bought any giant rats I've collected them from the other skaven kits I bought and have about 75 of them?)
I think that cover most of the units in the book (I might be missing something???)
Skaven are a great army and super fun to play. They are going to misfire and blow themselves up a lot. Run away and blow up (slaves) don't be afraid to sacrifice units. Everything in the skaven army is expendable haha
If you have any other questions just let me know I can help you as best as I can. Always glad to help someone who wants to join the verminous hordes