I use a wood comb from the Body Shop as well as a brush sometimes (my hair doesn't tangle badly so combs don't cause much damage for me).
You hair doesn't look so thick that the combs you named should be any issue. What is your hair's circumference though?
A number of people here love the Tangle Teezer but I have no background with that so I can't say how well it would work for moderately thick to thick hair hair.
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