Welcome!
I always liked the idea of playing Nidalee as an AD Bruiser. Her Catform is really strong in melee and it scales well with AD.
I usually played Nida as a Support on the bot lane and was busy throwing spears, healing and laying traps. It works quite well to be honest. With these Spears you can wreak havoc on the enemy carry/support since they do a super high amount of damage with a little bit of early AP.
The problem is: Mana
If you want to keep the pressure on the enemy you have to solve your mana problem since spamming spears is expensive
As a support you dont really earn a big amount of money so i usually went for the chalice of harmony to solve this.
Now you want to buy this chalice and wards and stuff and you dont get any more ap so your spears will fall off in damage early on and you are rendered nearly useless.
When teamfighting starts you are squishy as hell and you stay in the back, throwing a spear or two, not really dealing damage, nor soaking some kind of damage.
you dont have any aura items your team can benefit from so basically you are... useless

now my idea.
build her as a decent bruiser with ad support items.
check it out

Pretty much a mix of standard AD Bruiser and Support runes.
For early harrass you want a little AD and Armorpen, for your Support you want GP/10
Everything else is flat armor and magicresist to beef your defense up.

Well this depends on how you like to play.
As an AD Bruiser you want to harass with your autoattacks. Maybe you will have more range than their AD Carry but most of the times it will be nearly equal. So you wait for your enemy to go for a last hit, jump out of the brush and throw a spear to his face. this has to hurt a little so i went for some AD in the runes and masteries.
If he fires back at you, you have enough skills in the defense tree to mitigate that dmg and reg your health up with your items and masteries.

The more defensive masterie tree combined with early skilling of the healspell will give you a ton of sustain in the lane.

i've been trying and trying and trying and the order really depends on how the game is going.
you are ahead? buy zekes herald first. It will increase your harass dmg and your sustain through lifesteal and hp
are you behind? lot of ganks? buy aegis for the passive extra life reg and resistance. you will be able to soak a good amount of dmg in catform while your ad can hammer away

easy. you dont skill the spear at all, since you have 0 ap it will do close to 0 dmg.
Use your healing spell for the fighting, its a huge attspeed steroid.
try to drop traps under the enemy carry before the fight, the traps reduce armor and resistances, making him a vulnerable target.