You probably want to ult first, and then Zenith Blade in. That way, you're a bit safer from enemy CC, and they can't disrupt your combo as easily. Something to consider as Leona is that you can wait out your ult's stun and then Q the same enemy to keep them locked down, or you can ult one enemy and immediately Q another important target.
Either way, make sure you don't initiate alone. As a support tank without much gold, you're durable, but you're not 1v5 durable, like a fed Nasus or something. If it's going to be a 2v2 skirmish, you can definitely engage to catch someone out, and it will provide you and your ally with a huge advantage, but if it's going to be a 5v5 teamfight, don't initiate unless someone is there to immediately follow up your engage by dashing in or something. Ideally, target an enemy before you engage, so that your team knows you're going to do it.
(And speaking of 2v2s and such, I should probably remind you not to ult unless you're really committing to the fight. Don't do it if you're just going to trade; do it if you're going to secure a kill.)
And as for the last bit, if you're focused on protecting an ally, Leona can help someone else engage by just using her R to stun some enemies, giving your teammate an opening to use their engage. Then move up after them, and be ready to CC anyone who tries to dive your backline. But make sure your teammate gets followed up, instead of just letting him jump in and die. Again, tell them what you're going to do. Communication is key.