Hi all I have a question about a build for an elf Kensei samurai multiclass

Our DM allows us to take both an asi and a feat when we gain a ‘normal’ asi (fighter and rouge extra Asi’s don’t count) [you can have 3 to ability scores due to half feats but never more than 2 in a single stat] and this obviously allows for some extra leeway in certain builds (monk and barb multis come to mind) Point buy, wood elf (probably) btw, maybe halfling Whilst this character is starting at level 8 I expect them to get to at least level 11/12 and would like their power to mainly be around here (level 20 is cool but who actually gets to play there) My question is if I were to multiclass (still tempted by straight samurai) what kind of depth would I go? I’m mainly torn between 3

1. Fighter 2 monk x Perhaps the best for damage, this allows for archery and action surge and then just classic monk shenanigans, grabbing sharpshooter and just being a better monk (imo)

2. Fighter x monk 2 I imagine the character having unarmored movement/defence and the bonus action dodge/disengage is nice for a ranged character, at level 8 I would have a 20 in dex and elven accuracy/sharpshooter (undecided which)

3. Fighter 11 monk 9 At level 8 same as above but taking monk levels after fighter 11, in order for that juicy flavour (evasion, walking on walls, proficiencies) Kensei features

Any help is massively appreciated, cheers