You'll likely need one month's rent up front and 5-6 weeks as a deposit.
Once you've applied for a place, they may ask you for 1 week's rent as a holding deposit, which they'll deduct from the above if your referencing checks are all good.
Ask about gas and electricity safety checks - annually for gas, every 5 years for electricity. EPC for the property should also be noted.
Private landlords are great if you get a good one, but you won't know until you're renting with them, so try and find out why the previous tenants left.
You should be given the how to rent leaflet with your application form
References will be your employer, bank, previous landlord if you have one, maybe a personal one.
When you view a place, make sure you note any issues and confirm that you'll take a place subject to them being remediated prior to moving in.
Run a tap in the kitchen and bathroom to check the water pressure - you don't want to find you have a shower that dribbles or a bath that takes 3 years to fill!
Letting agents do 3 monthly inspections.
Double check with UC - if your daughter is in full time education, they're classed as a dependant.