What is their monthly income?
This is the first question to ask in order to determine the tenant's ability to pay rent. Ask for the after tax total income of the household. This is the amount of cash people will take their rent from. You can also ask about any additional sources of income - benefits, child support, food vouchers, etc.

What is their source of income?
This is a very important question. People who work and have stable jobs can pay their rent on time, whereas people who are unemployed usually depend on government benefits or their family's help. This means that their rent may often be late, or that they will prefer to live with many people in the property. This causes problems in terms of maintaining the place and leads to more wear and tear of the house. The best tenants are people who have stable professional jobs.

How soon do the tenants need to move?
The faster the new tenants move the better for you! This way you will minimize any rental losses by having the space empty. However, a serious applicant starts looking for a place well in advance and cannot expect you to sign everything and welcome them in during the same day. If you want to have some time to advertise the place again, tell potential tenants they have to wait a bit. If the tenant is willing to rent this is a sign of a responsible and problem-free tenant.

Why are they moving?
This is one of the biggest questions. Applicants will tell you the reason for their moving and based on that you can decide whether you want this tenant or not. People who are rushing and want to move immediately are usually the ones who have been evicted for not paying their rent to their previous landlord.

Do they have any prior eviction or criminal record?
This is one of those questions you wouldn't always receive a truthful answer to. If you want to be on the save side, do your own research and ask for contact details of previous landlord.

How many people are there in the tenant's household?
The bigger the family, the more wear and tear you should expect. You have the absolute right to charge more if you are going to accommodate a big household. Check whether the people moving together are related - a family, a group of friends, co-workers?  

How much are they currently paying?
If their current rent is close to yours, this is the ideal situation. If a whole family is moving together, they will probably have a higher income and can afford a higher rent.

How much money do they have for moving?
Ask this question specifically and directly. If you require a security deposit and rent for one month upon signing of the contract, but the tenant needs the money in order to move, it's better to reconsider. If you want to wait for them, however, insist on a higher deposit. You have all the right to ask whether the tenants have money, because there are many people who would try to pay only partial rent until they are settled down.

Do they have any pets?
It is up to you whether you wish to keep your property pet-free or charge a higher rent because of the pets. If you are renting out a rather small flat and the family wants to move with a few big dogs, this has disaster spelled all over it. If you don't have a backyard, the dogs will eventually cause damage to the place.