Bonnie, it depends ! :cat:
I have the Nikon D7200 and Tamron G2 150-600 f5-f6.3 which I just about always shoot hand held and carry around on a sling (it really helps). It's about as much weight as I want to carry, and there are the odd occasions where I'm looking for even more reach.
I think it's very much going to come down to personal preference. ie. How much weight and size do you want to handle is probably the most important factor, and what sort of shooting do you want to do and at what distances on what subjects? What sort of light will that be in? Bright only? Or all sorts of light including lower light where a stabilization system will help? Sometimes what sort of a deal you can find also comes into it.
Broadly, I think it comes down to more reach more size vs less reach less size. The extra mm have their unavoidable cost. Either way you would probably want to put the rig on a Black Rapid Sports sling or similar for maximum enjoyment walking around. Then of course you have to weigh up (literally) how much time you will spend shooting on a tripod or other fixed rest.
I think you choose your preferred compromise and either go 600mm or 400mm. Budget is either going to be there or there abouts. Beyond your budget, the Canon 100-400L IS II (the MKII version) is well worth considering stretching to. It's hard to go past the L glass for quality. Additionally, because this is a high quality L lens, it also takes the 1.4xTC reasonably well which would give you a 140-560mm f6.3 - f8 and a weight for the lens and TC combined of ~1.8kg (~4lb) , so that's something to consider as well.
The Tamron G2 150-600 is great fun. Make sure it's the G2 version. If you think it's heavy, then pick up the ~2 lb heavier Sigma 150-600 Sports (6&1/2lbs!) for comparison and then come back to the Tammy ...... it will seem light in comparison ! :cat:
Of the 400's, the Sigma 100-400 f5-f6.3 OS is a good versatile lens that is right within your budget. The Canon 400 f5.6L might also be an option. Both of these are around ~2 lbs lighter than the Tammy, though less reach.
Only a lb lighter than the Tammy 600, but near twice the cost, the Canon 100-400L IS II is going to offer the best quality of the lot. It's an investment piece, and only you can decide if the small improvement in image is worth twice the expense. If you ever upgrade bodies to the 90D, mythical and long awaited 7D III, or some future Canon body, at least you will have the comfort of full compatibility.
I think the best way to try and sort all of this out is to try and get the rig in the hand and see how you like the feel of it. One of them will speak to you. The 600's could take a few weeks to feel entirely comfortable handling and pointing them, but I'm happy with mine for BIF even. Shooting a 600 is pretty groovy :hippy:
Good luck !
Chosun :gh: