Creating responsive website with a grid - advice?

If you do opt for a grid framework, I'd avoid Bootstrap, and go with Foundation. 1) it is arguably a much better grid implementation, 2) its syntax is friendlier, and 3) a flexbox-based version is also available. Also easy to download a streamlined version with just the features you will actually be using.

Foundation | The most advanced responsive front-end framework in the world.

Skeleton is also a simpler grid framework with an easier syntax. Skeleton: Responsive CSS Boilerplate

In my opinion Bootstrap is an over-hyped framework.

There is no such thing as a univerally compatible framework or css layout, as it will always depend on just what you wish to create.

A grid framework is an hangover from when designers used fixed width layouts, and even though they have now been used to describe a flexible layout system, they are not really suited to a media that can be viewed at almost any width from a few hundred pixels to a 55 inch 4k tv screen, (or larger).

I would at the moment recommend using css flexbox for layout, but many people cannot come to terms with its use, as it requires a different way of thinking about how a layout works from the now traditional 'float' based layout. In the next few years there will also be a rise in the number of people using the css grid layout module, which is a css layout system and has nothing in common with the current grid frameworks such as Bootstrap.

All i can really suggest is try both css flexbox and css grid layouts, and compare them with the frameworks such as Bootstrap and Foundation, both of which are going over to use css flexbox as their default layout system, (which should at least tell you that css flexbox is worth learning first, even if you then move to one of the frameworks).