Hi Dougie, and welcome to the forums! Glad you're here
It sounds like you are doing great so far. The main thing to remember is to take it slow, and built a trusting bond with your bird.
Give your bird a few more days to settle into it's new home, and then you can start trying to tame it.
If you have any extra food and water dishes that you can add to the cage, this will help make sure that it finds them and is eating and drinking. Remember, budgies can be sneaky and you may not actually SEE it eat or drink, but there should be some empty seed hulls in the dish or on the bottom of the cage that will tell you that it's eating.
Sitting by it's cage and talking in a calm voice is a perfect start. Keep doing that
If you can post a picture of your new bird in natural light, and a clear shot of it's cere (nose) we can help you determine the gender of your new friend.