Here are two alternative ways of handling initiative. In both variants actions get declared before we enter combat, thus simulating the battlefield differently (and imo more "realistic" and fun) than the standard initiative:
1. Is based on Mike Mearls Greyhawk Initiative (see attachment), everybody declares and then initiative gets resolved based on their planned actions. Lowest roll goes first.
Ability modifiers are not used for determining speed but are deemed covered by their function in increasing damage and / or as prerequisite to use certain weapons or spells effectively.
While I can see that it's not a 100% accurate depiction of how weapons function in terms of speed, i.e 2H that is always slower than a dagger, the variant keeps in mind, that DEX based weapons (light, medium) are originally balanced around going earlier in combat due to being used by DEX heavy characters and the standard initiative being DEX based.
This argument extends to STR based fighters who use STR based weapons (heavy). They often have some DEX and therefore go 2nd. Spellcasters who mostly have low DEX go latest.
So the speed factors of weapons and spells carry over the original properties of the initiative balancing in an elegant way.
2. Is:
5E - Concurrent initiative variant; Everybody declares/Everybody resolves [WAS Simultaneous Initiative] (well worth to read the thread and @formerlyHemlocks elaboration on the variant)
The difference:
1. is for players that love the tactical "wargame" aspect of the combat and more crunch.
2. Ditches initiative completely. It is suited for players that love a more cinematic way of resolving combat but it works surpisingly well. It also makes people think outside of the "wargame" box.
I would say it depends on what you and your players like better. I playtested both variants extensively and they are both solid.