I would suggest going to a shop (either LQS or JoAnn's) and pick up just about every manufacturer's ruler they have. Pick out a bunch of different fabric colors that call to you. Ultimately these will be the colors you will go back to time and again. Lay the various rulers onto the fabrics. See which colors of lines on the rulers are easiest for you to see. Stick with that brand and get at least the 6 x 24 (or an 8 x 24 if available - works well for borders). I would also pick up a 6-10" long ruler by at least 3-4" wide...easier to manage when doing some trimming or small work. As for a 'square up' ruler...I only own a 12.5". I can use that on up to a 12.5 x 12.5 block to square or anything smaller. Make sure the main (6x24) ruler has at least 45 and 65 degree lines on it. They will become your friends.
While it's true that 'an inch is an inch is an inch' some lines may be thicker/thinner on the various rulers. Hence the recommendation to use at least the same brand throughout a project. Check to see that the rulers you like have 1/8" markings. As your quilting expertise progresses, you'll want these.
As to mats...I use a self-healing. Frankly, I don't care about brand either but I do have Olfas. I generally don't use the lines on the mat for measuring...I use the ruler. I place a perpendicular line on the ruler on the fabric fold. I then use the measurements on the ruler for cutting. Remember to keep the piece of fabric you want to keep under the ruler!
Just use the same method throughout your project whichever method you decide works best for you.