When installing wall cabinets it is not unusual to have cabinets that do not have any studs behind them. These should be supported by the cabinets on either side of them. Your best bet is to “mull” them together through the stiles. “Pony” makes a clamp called the “Cabinet Claw”; I believe they are now only sold in pairs. It holds the cabinets together and provides a drill bushing for a 1/8” drill bit. After boring the pilot hole, the bushing flips up and allows room to bore a counter-sunk area for the mulling screws. They also make this clamp for European style frameless cabinets.
The mulling screws should be a good quality wood screw, not drywall screws. The cabinet hanging screws should be designed for hanging cabinets; most manufacturers include these with the cabinets, generally 4 per cabinet. You should have a few extra to use with taller cabinets (only if there is a center hanging rail in the rear). Never hang a cabinet with screws that don’t penetrate the hanging rail, it will suck the back up against the wall and make it harder to install any cabinet shelf support clips that may be included with the wider cabinets.
If you are installing frameless cabinets, or just want a little more security with your face frame style cabinets, you can purchase “T”-Bolts. The good ones install with a hex key. Each half has a “T” cross section, one half has female threads and the other has external threads (like a bolt or machine screw). Drill the proper size hole through both cabinet walls, near the frame in the front, and near some shim in the rear. Slip the female bolt through the hole to line the holes up, and then bolt them together. Don’t really snug them down until all of the cabinets have been hung.
Hang the wall cabinets first. There are a lot of people suddenly advocating setting the base units first. I don’t know the logic behind that; even if you have a cabinet lift on the job, you still have to lift the wall cabinets up to the lift, and then work over the base units while securing them in place. By starting with an accurate layout, the wall cabinets will always be where you want them to be.
If you follow this procedure, there is no need for toggle bolts, molly anchors, or anything else that will make the finished installation look unprofessional.
When you come to a wall, face frame cabinets have about 1/8”- 3/16” of scribe space along the outside of the stile. You can us a block plane to make this follow the contour of the wall. It will slip right in without any gaps. Use wood shim or stepped plastic cabinet shims behind the cabinets, and on the floor below the base cabinets. You want to be sure that all of the cabinets are plumb and level; check for level from front to back on the base cabinets, as well.