My hair is pretty coarse, so I needed to experiment around for a while before finding something that worked. The main issues that caused nicks and razor burn for me were as follows.
* Overly frequent shaving. If I shave every day, I will get nicks and ingrown hairs, regardless of technique. After I shave, the skin slightly closes up around the follicle. Not enough to be fully ingrown, but enough that there's a bump of skin from about 12 hours post-shave to 72 hours post-shave. If I shave again during that time period, the razor will catch on those bumps and cause nicks. If I wait 3-4 days, the hair pushes out, and can be cut cleanly.
* Clogged razors. This is partly due to the coarse hair, and partly needing to remove 3-4 days of growth at a time. The blades of a cartridge razor are placed far too close to each other, and need to be rinsed out several times over the course of a shave. Sometimes multiple times over a single stroke. If this isn't noticed, I need to go over the same area again, increasing razor burn. While safety razors clog as well, it takes longer for them to do so, and it is easier to rinse out the accumulated hair.
* Over-use of cartridge razors. An 8-pack of cartridge razors is $25, where a 100-pack of safety razor blades is $10. I get about 2-3 smooth shaves from each razor, and it's an easy habit to replace a ten-cent blade every week or so. Even if I accept that cartridge's last longer, I can't believe that they would last the 35 shaves estimated by the marketing's 5-week estimation. Between the higher cost and the claimed lifetime, I would use cartridge razors well past the point of being dull.
So at this point, I have a reasonable routine: Replacing the blade of a safety razor every 7-10 days, shave every 3-4 days. But figuring out that routine requires going against the advertising, choosing an older style of razor, and avoiding the cultural expectation of daily shaving.