A drill press is great for getting holes square to the work. Many cordless drills these days will have a level built in to help get holes straight into a vertical piece of work. You can fool around with a pair of squares if you need to. Another option is to have someone, with a drill press, drill a hole in a piece of scrap material, even a wooden 2 x 4 is good enough. You can then hold that against your work piece & put your drill bit through the hole in the 2 x 4 to get your bit straight into the work.
Generally speaking, I like to have 1.25-1.5 diameters in steel, and 2-2.5 diameters in aluminum. I don't have a real number for G10, but I would think that 3-5 diameters might be a good target to start with and see what happens. If you go too deep & you don't tap first, then you will break the screw off. Greasing a self tapping screw will sometimes let you get it in a little further than it would go dry.
If you want to calculate the minimum engagement depth, start by figuring the cross sectional area of the minor diameter of the screw, then multiply that times the ksi figure for the screw material. You then basically do the same thing in reverse for the work material & add in a safety margin, like 1.2-1.5 or something like that. If I had specification values for G10, I could run some numbers for you. 304ss (aka 18-8) is usually around 60-70ksi. If you want to twist your head up with information about fasteners, you might start here -
https://www.fastenal.com/content/documents/FastenalTechnicalReferenceGuide.pdf If you want to get into it really deep, you can pick up a copy of the machinery's handbook.I think that the 30th edition is out now. My copies are much older than that.
If you need a drill guide block made out of something better than a 2 x 4, I can make one & mail it to you.