As to the property - look at the condition generally inside, does it look well maintained? Look for signs of mold in the bathroom etc. This will only get worse if it's visible already. Make sure everything works ok, switch all the appliances on and off, make sure things like the shower work ok.
With the AST - the agreement - don't sign anything there and then. Take it away and read it thoroughly. You should also get an inventory which should state the condition of everything in the property. Make sure this is up to date.
Ask where the deposit will be held. It's law now that the deposit has to be protected either in a scheme or by insurance. You should ask whether this will cost you anything.
Check what bills you will be paying, whether you or the landlord pays for the water etc.
Don't be pressurised. Is it a place you would want to live? Does the landlord or agent sound reasonable? Do you get the feeling they will be easy to deal with if something goes wrong with the property?
Have a look round the area. What are the neighbors like? Is it a decent area?
Finally, the rent. Check what you have to pay in advance, its usually 1 months rent plus the equivalent of 1 months rent as the deposit.
Good luck.