Standard on-hit Nut build, can be played either adc or mid, only recommended mid if you have an ability burst adc in duo (ie: chiron, ullr, danz etc.)
Can start either t1 axe or t1 bow. Buy however many potions you feel like you need. Cowl/gilded are also ok, but I prefer death's toll because of the crazy early sustain/mana sustain, and the cdr late game.
Tyrfing rush because it's the second best lane rush behind toxic blade, but on Nut specifically, it's really good because it super-juices her clear. Sun beam because it's a lot damage, although you can sub it out for toxic, o-bow, qin's or bragi's if you want. Riptalon, great stats, passive makes you very hard to take extended trades into, and 10% pen. Silverbranch, good yellow damage, and another 10% pen. Executioner is your big shred bomb item, obviously great into tank comps, synergizes with yellow numbers, contributes to other player damage from team mates because it's shred not %pen. Last slot largely flex/situational, can be qin's, can be hastened, can be obow, can be upgraded relic (aegis/shell usually, although blink can also work), can be berserkers/shogun's if you're extra spicy or into heavy phys/mag comps but usually I default to hastened because I highly value movement and kiting ability.
Can swap sun beam for toxic if into a heal/lifesteal heavy comp, or if you want more favorable 1v1 trades in lane.
Can drop hastened for o-bow, personal preference. I value the kiting and haste from hastened, and find that I still do enough damage in teamfights without the obow.
Can swap exe for dominance if you want, usually exe finds more value unless you're blowing people up in under 2 seconds.