Your idea of using a concrete slab is a good start. Since you want to have a raised edge the assumption is you want containment, and since you also want to be able to hose it down you want a draining/washable system.
Sounds very similar to what a food processing plant would do - so there are surface treatments you can make to the concrete that will allow you to wash it down even with chemicals.
Your slab should be poured with a grade - slant towards your drain system - and depending on how you want to handle that drainage i.e. sewer system or other methods should determine how high up the slab should be for proper drainage (for example a pump system or gravity system).
Given your requirements , for the drain you might want to consider a catch system or a trench style drain (basically this is a grate with a drain underneath) - the slab should slope its grade towards the drain. Or you can use a simple floor drain with a removable cage to catch debris (so your drain does not get clogged - with hair or other things).
You should use an Epoxy type resin coating to cover the slab there are many types available but if you look for washdown epoxy floor coatings there are several manufacturers and types available.