The Ikea kitchen cabinets are 24" deep. You will need to get a countertop that is deeper than standard vanity counters which are roughly 21" deep. I found a couple of remnants at the granite yard but I have not made a decision yet. It is a fairly small counter-top so the remnants were not particular attractive from a price perspective.

Many individuals love the deeper Ikea cabinets and I am doing the same thing in a bathroom. You need to determine what you want the cabinet to look like. My cabinet will be a 48" base cabinet. I am building this by using two 15" Ikea cabinets, one with 4 drawers and the other with two drawers; one 18" ikea cabinet for the center. The 18" cabinet will just have single tall door. I am planning to use a Duravit drop in sink which is 13" round. It is quite hard to find small sinks but I wanted as much counter space as possible.

If you are using the full ikea cabinet with doors, go to the base cabinet section

If you are getting your own doors made through Barkers, Scherrs or SemiHandmade, you just need to order the cabinet frames and drawer inserts as needed.
Ikea frames and plinth

There are a ton of threads on the kitchen forum about Ikea cabinets and there is also the Ikea Forums website. It is not difficult but there are a few things to understand.
Good luck!

One other thing to keep in mind is that IKEA is changing it's cabinet system early next year (I think February), so if you've planned to use this one, you should probably purchase soon.