TS, here is my take. Just a personal opinion, so don't take everything I say too seriously.
Personally, lens has a longer lasting value than camera bodies. In this digital age, digital bodies are like personal computers. They just get faster, higher resolution, better AF, etc. in short, there won't be a "best" time to buy camera bodies. Just get one if you need one - just decide if you need a full frame or a sub-full frame would suffice.
Lets get back to your lens. L or no L? L is the premium as in this is the way Canon has designed and marketed its lenses. If you have the money, just get the L lens. Reason is because if the lens has the right zoom range, you will not see the need to down grade to a cheaper price lens of the same range. Furthermore, the image quality will definitely be better than a non L and even if it does not, chances are the fault lies with the photographer's usage behavior. Visit
Canon EF 70-300mm f/4-5.6 L IS USM Lens Review for a review if you are interested.
I will not advise you on which to get but the 2 L lenses that I believed will suit you would probably be the 70-200mm f/2.8 L USM IS II or the f/4.0 of equal zoom range. The other lens would be the Canon EF 70-300mm f/4-5.6 L IS USM.
That is all I have to say and as a final comment, enjoy the process of photography and worry about gears later.
Dan