Most tapers place the metal corner bead first. This is primarily because if you were to do any taping first you'd have to wait until that dries to install corner bead. It's a matter of efficiency.
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It's also usually best to keep metal bead set snugly to the drywall, with nothing behind it. This allows you to keep it straighter and on plane. It should protrude just slightly on both walls when a straightedge is set against the drywall perpendicular to the bead. "Tucking" the tape under the bead does nothing of value. There's tape all over the building that's not tucked under anything and it's not an issue.
All that said, drywall taping is something of an art and you're free to do what makes sense for you and your project. Just remember the cardinal rule: lighter is better. The pros I've worked with do very little sanding to produce fantastic results, and it's far easier (and less messy) to skim on another coat than to grind down humps.
Drywall finishing is a multistep process that involves mudding, taping, and coating drywall boards to make the walls and ceilings look even. A handful of tools and materials create a professional drywall finish, such as the corner bead, which serves structural and aesthetic purposes.
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Drywall corner bead is an angled piece of trim installed along the length of outside wall corners, where two drywall boards meet. Corner bead is used in drywall finishing for two reasons: to stabilize and reinforce corners and to cover the visible seam between the two separate drywall boards, creating a seamless 90-degree angle.
Corner bead is typically only used on outside corners because it’s vulnerable to wear and tear. Although corner beads are used on inside corners, they aren’t necessary, since a simple paper tape installation will suffice.
Corner bead comes in a variety of materials and shapes for your finishing needs.
Metal is the most traditional type of corner bead. Metal corner bead is sturdy, so you can use it to cover up any flaws in the drywall board edges and create a crisp 90-degree angle, even if the drywall wasn’t hung perfectly straight. Out of all of the corner bead types, metal takes the longest to install because it’s thick and requires a lot of joint compound. Metal beads come in two shapes: square (90 degrees) and bullnose, which has a rounded edge for curved corners.
There are two types of paper-faced bead: metal and composite.
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