Whether the area behind your new house is just bare soil or it has been turfed, you may encounter similar problems: ground compaction, buried rubble, poor soil. It makes sense to tackle those first, before you start to create your dream garden. Your new lawn may be good enough (for now), but the border areas will need some elbow grease.
1. Break up compacted ground
Double digging would be ideal but failing that, using a digging fork, turn over the ground about 20 cm deep. Spread a bucketful of garden compost or similar soil improver over each square meter of the dug ground, add some general-purpose fertilizer, and fork it all in.
2. Remove buried rubble
Take as much out as you can whilst digging. It can be used to provide better drainage in high raised beds and any reasonably good bricks may be used as border edging. Remember that lime from cement and mortar makes soil alkaline and unsuitable for azaleas and other lime-hating plants.
3. Other options for poor soil
Consider raised beds, making sure the topsoil you bring in to fill them is of good quality. Or, buy a suitable seed mix and create a pollinator-friendly perennial flower meadow full of plants that thrive in nutrient-poor soil.
On very poor ground consider raised beds