You've gotten excellent suggestions from everyone so far. I'll be so bold as to do a quick re-cap in no particular order.
-Put your index finger on the top edge of your cutter
-Use at least a small piece of painter's tape on whichever side of the line on your ruler you decide is where you want to cut. (I've advocated this for a long time and only recently started practicing what I preach - way too easy to have not done so sooner).
-Use your ruler to measure vs your mat. If you are having to make cuts larger than your ruler width, I'd do a slightly larger cut and trim up my unit/block as needed. You can butt 2 rulers together but I personally have not had much luck with this method.
-Keep one finger off the ruler onto the fabric to help hold the ruler steady. 'Walk' your hand up the ruler as you cut, keeping that pinkie finger on the fabric and the rest of the fingers on the ruler the whole time (sounds harder than it is).
-Use the same brand ruler throughout your project. If you need to re-purchase rulers along the way to accomplish this, it's well worth the expense - but use a coupon!
-Check your table height. There are lots of 'erognomic' sites out there to give you hints as to how to measure the best table height compared to your height. If you are stretching a lot to make cuts, likely the table is too high for your body height.
-I'd also recommend getting some of the clear rubber sticky dots to place on the 4 corners of all of your rulers. It helps grip the fabric and reduces chances of slippage.
-Slow down and take your time. Take a deep breath, relax!