The powerful LED strips need a lot of current and are very bright. Three across a 4m width seems more than adequate for me. I've found the best way to fix them is to paint or prime the surface, then stick on a length of 50mm wide aluminium tape (the stuff used to join insulation sheets), rub the aluminium tape down well and then stick the LED strip down the centre of the line of tape. This makes the LED strip adhere better and also seems to make the strip run a bit cooler, which in turn helps the self-adhesive backing stay fixed.
For power supplies, I've used ventilated aluminium cased 12V supplies, wall mounted. The bright 5630 strip needs about 3A per 5m length at 12V, and I opted to use three 5A supplies, like these: http://www.ebay.co.uk/itm/12V-24V-IP67-Waterproof-LED-Transformer-Driver-Power-Supply-CCTV-240V-DC-2A-5A-/291663843407?var=&hash=item43e885104f:m:mp4HSAn6fw0MWK4ZUIErztg
I ran lengths of 1.5mm² T&E cable above the ceiling to feed the far end of each strip (I've used the full 5m on each roll) joined to either end of the strip and then with single 1.5mm² T&E feeds running to the power supplies, inside a length of conduit where they come down the wall.