Initiative: how I'm doing it currently

Here's how I'm doing initiative in my current house game.

Every combatant or "fire team" rolls 1d20+ initiative mod + a fighting bonus on the first round they are able to act. (a wizard and a charmed fighter is a fireteam as is a squad of like men-at-arms or monsters )

This initiative score is recorded and maintained for 5 rounds, when 5 rounds are over there's a re-roll. We use 12 seconds rounds so 5 work out to a minute.

Combat is conducted on a countdown each round starting high and going low, ties are simultaneous so it's possible for 2 combatants to kill each other on the same initiative count.

We have parry rule that allows one to specifically defend against attacks. One can't parry an attack before their initiative count comes up in combat unless: they have a much longer weapon then a foe, are armed with a sword and facing a single foe (after the first round of combat) or have a shield and some defensive spells may be cast out of order.

When one readies a weapon during combat their initiative is reduced by their weapon speed. Some allow an attack on readying, some don't allow an attack until the new initiative count.

If one is harmed during a round their initiative score is reduced by 1 and only 1 regardless of how many blows are suffered in a round.

Some actions and failed actions can reduce initiative as well.

If the initiative score is reduced to less then 0 one can still act in a round but their attacks, saves and other such checks suffer a penalty equal to the negative initiative score. If one has a negative initiative on the initiative re-roll (after 5 rounds) they suffer a penalty of 1 on that roll.

Being encumbered halves ones initiative score.

Initiative has a very telling effect on combat as it limits ones defensive actions and gives the attacker with the advantage a decided advantage. Shields are darned handy and the sword is given a coolness factor (that is strictly for genre emulation).
No one wants to drop a weapon because of the disadvantage it subjects them to in readying a new weapon.