If I could only have 2 rulers I would choose a 6 inch X 24 inch, and a 6 inch by 12 inch. Both of mine are by Omnigrid. My only requirement for a cutting mat is that it be self-healing. I, personally, only use the lines on the cutting mat for lining up fabric - not for measuring or cutting.
You should always use the same brand of rulers (omnigrid, Olfa, etc) throughout a project because the width of the markings on the ruler could be different among different companies. As far as which brand to buy, that is personal preference. Some have black and yellow lines. Some only have black. Some have 1/8 in markings and some do not.
If I were buying now, I would like to try the Olfa frosted non-slip ruler. I would like to see how 'non-slip' it is. I have added Invisigrip to my Omnigrid rulers to help prevent slipping.
You do NOT have to have a specialty ruler to cut triangles! However, you will have to learn the rules for calculating the size of strips, squares, etc. for cutting various types of triangle - 1/2 square, 1/4 square etc. Some of the triangle rulers are useful but really not required. I have both the easy angle and the companion angle rulers but have only started using them recently.
Buy what you can afford.