I currently use the Canon 100-400 Mk2 and/or Canon 300 F2.8 L IS as my walkabout lenses. The 800mm is mainly for hide use! I have also tried out/used the Tamron and Sigma 150-600 lenses as well as (previously owning) the Canon 600 F4 L IS and have used the Canon 500 F4 L IS Mk1 and Mk2 quite a bit.
Personally I would go for the Canon 500 F4 L IS Mk1 or 2 - but they are quite big and pricey! Having said that they are one of the best long lenses out there, including the competition.
The Canon 300 F2.8 L IS Mk1 or Mk2 is simply a superb 300mm lens in every respect - but it is a 300mm. You may find that you have to resort to extenders quite a bit. Now the good news - it works rather well with them! The Canon 1.4 Mk2 or 3 works great with little loss of anything except 1 stop of light. The 2 x extender needs to be used with a little more care and is more light dependant. Not necessarily the amount of light but this combination does benefit from contrasty light to get the very best out of it.
I should have said at the top of this post that my cameras are the Canon 7D2 and 1DX.
The 100-400? Best lens of it's type - end of in my experience. On my 1DX it is simply great in AF and IQ - no it is not as good as my 300 F2.8, but what is? However it is light to carry about, very versatile and takes a 1.4 extender decently. Whilst the 100-400 Mk2 performs very well on my 1DX it is not quite as good on my 7D2. I don't know why as it focuses very accurately but just doesn't give the same sharpness/detail as it does on the 1DX. I think that this is down to my individual cameras and lens - if you want to see what the 7D2 can really do with this lens then have a look at "Pondrader"'s posts on this forum.
These are just my thoughts and observations - certainly not Gospel! I would point you towards the 300 F2.8 L IS Mk1 (not silly money) or, if you could stretch to it and it isn't too heavy, the 500 F4 L IS. Having said that the 100-400 Mk2 is lighter, cheaper, more versatile and does a very good job - just not quite (but nearly) as good
Life is for living, cameras are to capture it (one day I will learn how!).