Zhul'Kari has a bunch of low rarity troops that make it relatively easy to get early power stars in to make it your best tribute anyway, plus you'll want to level it to 10 first because of the magic bonus. A gold starred Zhul'Kari gives as much glory per tribute as a silver-starred or below Whitehelm anyways. My friend used primarily Dragon's Claw team in early game and therefore got his Dragon's Claw to gold star first, so that was his home kingdom (again, beating out Whitehelm in glory tribute anyways).
In my experience, Whitehelm is a bad option super early game because the investment needed to make it the best glory tribute at any given takes away from areas that actually help your early game progression - like making an effective early PvP team and unlocking magic skill bonuses.
Overall, it matters very little, especially if you spread out your kingdom levels early on to maximize your tribute chance, which has a much better cost to benefit ratio of rushing one to level 10 (unless said kingdom gives a worthy skill bonus, like magic, and you can get it done in a few days). Multiple kingdoms giving tribute at the same time give gems, which are much more useful both short and long term than squeezing a few extra glory out of your tributes, as well as gold keys. If you are in a guild, you should be getting "enough" glory to at least unlock the weekly troops with very little effort, even just starting out, and it will be a while before you start mass buying them to stock up on arcanes.