but make sure that those appliances are ventilated. dont want a build up of gasses or stuff when that partition is built.
Go to Home Depot and buy their "home improvement" book, there you will find different ways of building partition walls and how to attach the sole plate to concrete. Your job is not difficult and doors can be added easily since you are building the walls together. Just make sure that the walls will allow a service person to work in there, make sure that the doors are wide enough for equipment to enter, like a new water heater. Just think forward on your project as to what might have to come in there for repairs/replacement.