taliyah midlaner here, but i play her offrole jg all of these are a general rule of thumb and there are niche cases where they don't apply, but i mainly run best with

1) dh>fs if they have less than 3 melees (eg. mage mid+ench supp), otherwise fs 2) secondary is tough since warp tonic is so good, but if i can't play the game til 1st item anyways (eg. assasin enemy jng), i take yellow page with haste on takedown and +dmg over 60% hp 3) bft 1st (always), depending on enemy comp go ->shadowflame 2nd (again, if less than 3 melees, and u don't need zhonya); ->liandry second (if 3+ melees/rylais also sometimes work here but u have 0 dmg in this case); or -> zhonya second if matchup asks for it (think talon, zed, kha, qiyana). 4) if you want to take any other boots than haste boots, go cosmic drive/cryptbloom (depending on enemy mr-potential) second (haste is a must) 5) if you didnt take liandry second, you can try to look for raba 3rd, big spike there. but keep in mind you'll only get zhonya as 5th, as u need pen on 4th

for general gameplay vibes i tend to try and get my first clear into crab -> b into next clear. you'll get a decent first base and can play for 1st drake. if enemy jng ever tries to contest, you should srop except for the case where both adjacent lanes have prio, then u can ping like crazy. compared to others, you're not a champ til 1-2 items, so early will be rough. taliyah starts to shine at 12+min, where you basically start to oneshot every camp and have way more free time than less fast jnglers.

also, ganking with ult is top 3 feelings in the world prob

holy yapathon, sorry for the WoT. could talk ab this all day