It is common for a landlord to ask for proof of your employment when agreeing to rent to you. If you want to share your employment contract with your landlord it is polite to ask your employer prior to doing so, especially if there is information in the contract that is not public, such as internal emails.
Landlord's can rent the property to whoever they wish and in order to make this decision it is common for landlords to want to see bank statements for the purpose of proof of income and previous rent payments. If you are worried and want to maintain your privacy you may redact areas of your statement you wish to keep private e.g. black out everything aside from income and bills or you may alternatively ask the landlord to use an independent reference company.