Initially, I would just use what you've got and see if the results are up to your expectations. If not... or just to see what might be better, start doing some research based upon your particular needs.
With a 50MP camera, the key question will be if the lenses have adequate resolving power to keep up with the sensor. You can find some lens-to-lens comparisons online (though they will have been tested on older camera models) at sites such as
http://www.dxomark.com/ and
http://www.the-digital-picture.com. There you might compare some of the latest and most highly regarded lenses against yours... such as the 24-70/2.8L II USM vs your 24-105L, and the 70-200/2.8L II IS USM vs your 28-300L.
http://www.lensrentals.com also does a lot of lens testing, but they only publish results with a limited number of lenses (they were quite impressed with the 24-70/2.8L II, though).
I hardly think the new cameras will only work well with "L-series". There are some superb lenses that aren't L. For example the EF 100/2.8 USM (non-L, non-IS) pretty much matches the newer 100L Macro for image quality and build... and is faster focusing, identical build to the 180/3.5L. Also the 45/2.8 TS-E and 90/2.8 TS-E aren't L-series, but are identical build to the original 24/3.5L TS-S and both the 45mm and 90mm have image quality rivaling that of the TS-E 24/3.5L II and TS-E 17/4L. (I especially mention the macro and the two longer TS-E lenses because I personally find them very useful for product shots in studio.)
Another example, for max image quality and sharpness edge-to-edge, I'd buy the EF 24/2.8 IS USM or 35/2 IS USM over the EF 24/1.4L USM or EF 35/1.4L USM. If I were a photojournalist, I'd get the f1.4L lenses instead. A portrait shooter might want the EF 85/1.2L USM, but for sports or any sort of action shooting the EF 85/1.8 USM is faster focusing.
I wouldn't even rule out third party lenses. There are some truly excellent ones, such as Sigma's "Art" series. If willing to focus manually, many of the Zeiss ZE lenses are superb, too.
My point, though, is that I wouldn't limit myself to just L-series lenses. Depending upon your particular needs, something else might be a better choice.