Scarpa is primarily a boot company, and the Apex is the sort of no-nonsense shoe they're apt to make. Kind of between the Salomon and Montrail shoes in 
Best gear for a 100-mile hike in the summer?
I did the 93-mile Wonderland Trail around Mount Rainier last summer. A lot of what you ask depends on where you are hiking. Is it likely to be cold at night? Will you likely encounter bad weather (we had a snow flurry in August)? Is the trail level and well-maintained or will you be bushwacking through heavy plant growth and having to scramble up slopes?
There is a lot of personal preferences with stuff like this, but here are my picks:
Packs - For light and fast, I love my Kelty Shadow. It is very light, but still has plenty of pockets and padding. On the Wonderland, I took my big Kelty 50th Anniversary Special (6500 cu in) external which comfortably handled a 50lb load on long trails. For what you are talking about, you will need to carry at least 25-30lbs and probably want at least a 4000 cu in pack.
Shoes - After trying a wide range of hiking boots with varying results, I have settled on the REI Monarchs which have proven comfortable and rugged. If you are carrying a heavy pack, you will want the ankle and arch support of a hiking boot. You are asking for a sprain with trail runners. Trekking poles can take a lot of strain off knees and legs.
Stove - the JetBoil is the biggest backpacking invention since GoreTex. One of these puppies can boil a liter of water in 2.5 minutes, they use minimal fuel and pack up nice. I have stopped camp cooking entirely and just carry a JetBoil with freeze-dried food.
Water - Water is heavy. You don't want to carry more than a gallon at a time (less if you can). If you are away from civilization, you will need to filter water out of streams and lakes. I like my SweetWater backpacker filter because it is easy to pump and easy to clean. I carry most of my water in a 3-liter camelbak bladder (max capacity, min weight) with an extra 1-liter Nalgene bottle to drink out of in camp.
Don't forget electrolytes (the salts and minerals you sweat out). Some people carry gatorade or Gookinade packets, but these can be heavy and bulky from the extra sugar and flavors. Elete electrolyte concentrate contains enough drops for 16 liters in a little bottle the size of TicTac box.
Clothing - Avoid cotton. It does not try quickly. Synthetic cloth (nylon, polyprop) are the way to go (but becareful around fire) because they dry quicker and wick away moisture. Those zip-off pants that can turn into shorts are great for backpacking. Avoid carrying too much clothes - mix and match so you can dress in layers depending on the weather and always keep one set dry at all costs to wear in your tent (wet = cold). Invest in a really good rain shell (waterproof, comfortable, breathable). Marmot has some good ones - so does REI.
Tents and sleeping bags - If it is going to be warm the whole time, you can probably get by with a little fleece liner bag and one of those little emergency solar blankets as a fall-back. Many ultra-light packers go with just a tarp for cover - more power to them, but I prefer a little protection from bugs and wind. Many of the solo backpacker tents are only 3lbs or so (like the Sierra Design Baku). Or compromise and go with a bivy sack.
Depending on your strength, conditioning, and the trail conditions, you can carry about 50lb max and still be happy. Carrying less is always better. Unless you are really really roughing it, it would be tough to get under 35lb for a multiday backcountry trip.
See the gear guide on Backpacker magazines website for other recommendations (below).
