Shaving after a shower, shaving every other day, I can get a lot of usage out of a modern safety razor, i.e. weeks with the same cartridge without much irritation. My yearly razor costs are already low at this point, and the effort of learning how to use a straight edge just doesn't seem worth it.
Check the reviews of your razor on varies shave forums to make sure it's not an aggressive razor. You may need a new razor.
Get good blade. Varies websites sell blade samplers, get that and see which blade works best for your skin/hair.
Get a good tallow shave soap. Don't use shave gel/foam. Use brush to make good thick foam. See youtube videos for help.
Wet your face with warm water before shaving, or some people shave after shower.