I'm new to using a router and have been experimenting with basic cuts on a table. I have not tried a handheld or freehanded on the table. I recently did all the cuts to make a serving tray and I want to cut out the handles. My plan was to cut two holes with a forstner, jigsaw between the two and then clean it up with a router. What is the safest way to go about this? Table or Handheld? Bit type, size and technique?
There are many ways to do this, any of which can be made safe enough for the risk to be acceptable. I'll outline how I would do it, but there are probably a dozen slightly different variants that would also work just fine.
I would use a template bushing on a plunge router with an oversized template to make the opening.
Start by determining the radius on the corners. To my eye this looks like about 1/4", so use a 1/2" (diameter) bit. Find a template bushing that is big enough to fit the bit inside and attach to your router's base plate (making sure it's centered properly - your bushing set should include centering mandrels that fit in your router's collet.)
Next you'll make a jig with a hole in it. The jig's hole should be oversized in both directions by the difference between the diameter of the bushing and the diameter of the bit. I'd make this template by ripping two strips of scrap to the height of the hole plus the offset, squaring the ends, and gluing them between two more longer strips of the same scrap. Marking out the center points of the hole before you glue it up might be helpful in alignment later.
The jig can be attached to the work piece either by clamping or with double-sided tape. If you plan on clamping try to make the jig big enough for the clamps to be outside of your router's base plate. It's no fun having to stop to move clamps around.
If you don't have a plunge-able bit you will have to start with a pilot hole. You might also want to hog out most of the waste to save wear on your router bit and make the cut a little safer and less tear-out prone. If your work piece is thicker than 1/2" you'll want to make the cut in stages. This will be a through-cut so make sure you're working on a sacrificial surface (and you don't plunge through it!)
Place the bushing against the inside surface of the jig, turn it on, and plunge the router into the work piece. Move the router around the jig in a clockwise direction. The router should be moved fast enough to avoid burning but not so fast that the motor bogs down or you feel like you're "forcing" the tool.
Remove the jig and run a bearing-guided roundover bit around both sides (again in a clockwise direction.)