Re this:
... the first step is to convert my footage to Rec.709 color space ...
This is wrong. If you do it this way, then you can make your life easier by having the camera do the conversion for you; that way, the footage you edit is 709 from the get-go. In other words, just set the camera to shoot Rec709. Which, of course, negates the whole concept of log.
If you don't fully understand what Log is for, and how it works, then you don't need it -- make your life easier and turn it off. But if you want the benefit of Log, then you need to do your colour grade BEFORE converting to Rec709.
You can try this for yourself quite easily. Shoot something with, say, really bright highlights, like clouds in the sky. Pull it in to Premiere, add a Lumetri effect to convert to 709, then add another Lumetri effect to pull the levels down. Done that way, with the 709 conversion happening first in the image pipeline, you should see the flat white sky turn into flat grey. Swap the order of the two Lumetris, and the sky should show real detail.
As for which LUT to use, and where to get it, see my reply in this post:
https://community.usa.canon.com/t5/Professional-Video/Is-there-a-standard-C-LOG-to-REC-709-LUT-for-c...
