Oh goodness me, I think I own almost every ruler out there. My family buys them for me as gifts. If the project requires a specialty ruler, i get it. I know, spoiled I suppose but there is a place for them when working on certain projects.
As a beginner, I love the 6 x 24 ruler and the 6 x 12. Then my second purchase would be a 6.5" square up ruler and a 4.5" square up ruler, and a 2.5" square up ruler. These rulers can come in packages sold as such.
As for preference on brand, I prefer the yellow and black lines of Omnigrid. I can see them the best thru all fabrics. I find that the clear ones with black lines are hard to see when cutting my black and white fabrics or a dark fabric.
I have learned that using the ruler to cut is faster and more accurate. I love to do minature quilts and using your mat will mess it up for sure. You cannot get an absolute accurate cut from the mat. I have a friend who does nothing but cut from the mat. She looses her points quite often in her quilts or she has to recut or fudge, plus takes her much longer. They call me Mrs. Edward Scissorhand because I can cut a quilt twice as fast as anyone else in my group and just as or more accurate.
Also, on the rotary cutter, that is a definite personal choice no matter what. I use the Fiskars rotary cutter because of how it sits in my hand, so much more comfortable for me. There are those that love Olfas and swear by them. It is how you like to hold them. be sure to try them out if can to see which one cuts better for you. My first one was an Olfa and I sliced the side of my finger right on down the side. Had no meat on my finger for quite some time. I then got a Fiskar and have not had the problem at all. It is all in the way you can handle it. I cut it years ago.
As for mats, since I cut by ruler, the self healing mat is about all for preference. I have not seen the the other brand of mat so I can't say how it is, but I may purchase it next after I wear out the other three the family bought me.