Shiny New Lots to Do

Hi, this is my first post, though I have been reading for a week or so.

I have decided to tackle my garden and do something productive with it. I have never had much interest in gardening, I suffered with hay fever for many years, which always kept me out of the garden. But I seem to have outgrown the worst of the allergies and would really like to grow food with my two small children, the eldest of whom is really interested in helping, he is four.

I have a south facing front garden with a lawn and three small border beds, I have a tall hedge and tree that keep one bed very shaded and damp.

In the back I have a thriving apple tree and several blackberry bushes, neither of which can I claim credit for, the apple tree was planted by a previous owner and the blackberries are wild. My ex-husband started growing potatoes in a bin, but I haven't done anything with that, not even looked inside. I may have to start from scratch with that.

Most of the back is paved, but there are three large-ish beds, one of which is against a very tall wall and is slightly raised. My cat is buried along here, I am not sure what to do about that! The blackberries are along here, I was hoping to tame them a bit as one in particular is growing out onto the paved area, so any tips on cutting that back without harming it would be gratefully received. Any foods that grow well up walls and in sun would do well here. I was wondering about beans.

The other two beds are terribly overgrown. I have a large rose bush and several other unknown plants but I really want to get rid of the lot and start from scratch. I was thinking of raising the main bed and using it to grow vegetables. It gets good mid-day sun but is in the shade of the house by early evening in summer.

I already have one large compost bin, I don't have much space for a second, but could possibly find space during the clearing process. I read something about turning the compost to help it rot down faster. Can anyone tell me more about this please? How is it done? I've had it for about 18 months now, never used anything out of it and it is about half full. How do I know when it is ready to use?

I'm assuming that, given the time of year, the main thing to do over the next few months is clear and prepare the garden for planting. When is a good month to start planting?

Thanks in advance!