Being a lefty in a righty world, I found the best thing I have is a ruler with a lip on it- to provide support for cutting. Line the lip up with the end of the cutting mat, it provides some extra "holding power" as you cut.
Scissors- I use Gingher scissors, since they are righty scissors (I never could get the grip of using lefty scissors) but very good quality, they slice like butter through the fabric.
I guess I trained my brain to "think" backwards with the numbers on the ruler- one trick I use is to turn the ruler to measure where I need it to be, notate in brain where it is on the cutting mat, then turn the ruler so I can cut, using the cutting mat as the giude. This is where the "measure twice, cut once" rule comes into effect, since there is greater chance for error. I've done the old 1" measurement error more than once over the years. But it works because the ruler is anchored and won't slip (referencing the lip ruler above).
Good luck!