I have to be honest and tell you that I let my 3 cats out within a week of moving house. I was planning to leave it 4-6 weeks but they settled and bonded with the new house incredibly quickly, plus I know their personalities and their love of food so I knew they would come back when called - they always have. I basically took it in stages. I have no back garden but a large yard and gated access to a large alley which is used as a communal meeting place for the residents of my street and has benches, hanging baskets, flower beds etc but is alley gated so can only be used by those that live there (who are all fortunately cat lovers).
The first time I let each cat out individually under my supervision for 5-10 minutes. Then I took them back inside. I did this every day for a few days until they stopped being keen to come back inside but showed signs of wanting to explore further. Then I let them out together as I know that the boys especially like to stick together when outside. I always left the back door open (despite having a catflap in it) in case they got freaked - which they did several times in those early days as they met the dozens of other cats that live in my small street. At first (6 weeks or so) I only let them outside when I was home in case they got into trouble and I came running to rescue them from other cats numerous times as there are a couple of bullies out there and my cats are wusses
It was spring so that was ok - wouldn't fancy having a door open all winter though!!
I was worried that they would get lost at first, especially as one of my boys was only 8 months old at the time and a bit of a jump first/think later type, but the older male stuck with him when outside and my female never goes far away.
I think that the first few trips outside supervised are really important to get your cat used to the smells of your new garden etc so I would try and use a harness if I were you, although they are not inescapable.