The quicker would be to get a close-up of your logo with a good contrast and to use the “vectorize” option.
The more accurate way would be to work from a close-up of your logo, and draw on the top of it.
If you don’t have a base image, you can draw it from scratch use the grid (shortcut = #) witch allow you to align objects with magnetism. I you want precise disposition, Inkscape has a good alignment tool.
I think boolean operations will be ok for the base of your logo (Draw three circles, decrease opacity a little will help you to arrange their disposition so that the center shape will form your shield. Select all three circles and use “Path>Object as path”, then select the circles two by two and perform “Path>Intersection”)
Rounded corners can be achieved by direct modification of the nodes, or using contract “Ctrl + (” and then expend “Ctrl + )” several times.
Use the same method to draw the curves (draw it from circles and boolean operations, arrange it on the top of the shield and carve it in the shield using booleans).
As your file will be light in weight I would recommend to duplicate (Ctrl + D) your objects at each step, so you will be able to start from a previous point without re-doing all of it again an again )
Just ask if you need more help.