Optimising Rogue and Fighter Multiclass 2024

How would you optimise a rogue/fighter multiclass in 5.5e?

Level 1 start Rogue as that gets you more skills.

Highest ability = Dex

Next Highest ability = Con (you will be getting hit)

Have Strength at a good ability number. but does not need to be the 3rd best.

Background is based on what you want decent abilities in, 

Weapons should be Dex based (Bows/finesse/light/etc.)  Concentrate on these types.

2nd level get Fighter.  You lose out on Heavy armor proficiency, but then I don't see a Ftr/Rogue needing or even wanting heavy armor.

Are you planning to be mostly rogue or mostly fighter? (Going anything close to even is not gonna serve you well. Both have central abilities that scale on class level.)

What is it that you want out of the other class?

Loaded question. Rogue/Fighter is one of the most common and potent multiclasses, and there are a number of ways to build such a character.
Baseline, start Rogue to get more skills, and reach at least level 3 in the class you want as your secondary to unlock a subclass. Whether you want to go higher than level 3 with your secondary class depends on what you're aiming for.

It really depends on what you're optimizing for, and also what level you're targeting. There are actually a surprisingly wide number of viable mixes at higher levels.