I don’t use tables. At all. I’ve heard of some people (still) using them but I don’t. I generally go with display: inline-block or float.
TBH, I’ve never really cared for grid “frameworks” or at least one that someone else wrote. My knowledge of their inner workings is simply not intimate enough for me to do what I want, quick and easy. I always hand-roll my own grid system and Chris has a great video on this here:
https://css-tricks.com/video-screencasts/115-dont-overthink-it-grids/
Now, this video really only covers the basics and there are many ways to go about it. This will give you a strong foundation though.