The first level of Theme Hospital is an easy one - you've simply got to cure ten patients. The diseases you'll encounter are all pretty straightforward, but it's important to get them diagnosed as quickly as you can.
You should build one of every room you can, starting with the diagnosis rooms like the GP's Office and General Diagnosis - although the Ward isn't strictly necessary. This level has plenty of space, so you should be able to build everything you need. Finances shouldn't be a problem either - your starting budget is more than large enough to cover the cost of these basic rooms.
When it comes to staffing your hospital, look for applicants whose skill level is more than halfway along the bar; these doctors and nurses will be more efficient when it comes to treating patients, while good handymen will clean up spillages and repair equipment much faster than lower-rated applicants.