Whilst LL's do have every right to decide who lives in their property and who doesn't, its also very often idle lettings agents who put this stuff down automatically.
It is well worth seeing if you can speak to the landlord of a property, if you can supply references from previous landlords, offer a bigger deposit or some other attractive clause to the contract such as professional carpet cleaning..
For pets, if you can demonstrate that you are a responsible pet owner, for example show that your pet is insured, is trained (certificates from training classes, report from a behaviourist) or that you have taken some instruction on being a responsible owner (seminars/lectures etc) and again, offer a bigger deposit or cleaning or both...
Then you stand a better chance.
As far as DSS goes - sadly, that can be such a pain if you get a crappy tenant - you have to wait until the tenant is 8 weeks in arrears before you can force the LA to pay their housing benefit directly to you.
If, as happened to me, they then do a bunk before the end of the tenancy, you lose out on whatever is outstanding from the end of the contract AND that first 8 weeks as well - so on a six month contract if the tenant does a bunk a month before the end, you only get three months rent and thats if the HB covers the full rent. If it doesn't and the tenant doesn't pay, you can whistle for it, theres no way of getting it out of them and a small claims court can order them to pay... but they won't!
Mine even had the cheek to ask for the deposit back (not a chance, not with the state she left the property in never mind the outstanding rent of over £1400! )