I wouldn't worry about the contract it's normal, if you're there 3 years there won't be any issues extending it. It can restrict you a bit if you want to leave before the 3 years are up, but also protects you at the same time. The usual alternative is an open contract where you both have 30 days notice. I wouldn't pursue a 4 year contract.
With regards to healthcare it's difficult to say. Some of the private hospitals/clinics are very good, their doctors are trained in Europe/US and is usually easy to get an appointment quickly if necessary. My experience of UK healthcare (NHS) has been very good, but I guess if you've been stuck on a waiting list for surgery for several months then got an infection while you were a patient, you may not feel the same way. It's fine here for fairly routine stuff but I think I'd be inclined to head back to the UK if a life threatening illness came along or anything requiring a complex diagnosis.