As your team's jungler, you are almost solely responsible for guaranteeing the rift's neutral objectives. Smite does a flat amount of true damage to monsters and minions that typically outdamages most champion's regular abilities. For this reason, you will always take smite. (sidenote: you are welcome to take Smite on D or F, but in high elo, D is a must ;))
Flash is one of the most useful abilities on Fiddlesticks. In addition to being a potentially life-saving ability, it is also extremely versatile. Level 3 ganks are made even stronger with a quick -->(Q). Level 6 ganks are made even stronger with --->. You can even "whiff" your ult and not hit anyone directly with it, be running after them, and flash into Q range to still catch them.
You could make an argument that can be very strong to help stick to people after you ult, but ultimately (see what I did there?), Flash is just a more dependable and safer option.
Helps you to keep up with enemy jungling clears. Keeps you moving around the map quickly to set up ganks and take objectives. Take savagery if you want to speed up your clear a little though since it buffs your W (drain) against jungle creeps.
In my opinion, the only option for a jungler.
Merciless > Meditation
Helps to finish off low hp enemies. Also, for the most part, your mana should be fine with the runic echoes procs from your jungle item combined with blue buffs every so often. Mana regen really isn't a problem anymore with this season's jungle changes.
Greenfather's Gift > Dangerous Game > Bandit
I suppose you can take one or the other here. For me, dangerous game doesn't really offer me much since Fid can heal everything back between skirmishes or teamfights anyway. Bandit is really made for supports imo.
Precision > Intelligence
Some might think the extra lethality from Precision is a waste on Fid, but personally I think opting for 5% extra cdr doesn't really do you any favors either.
Thunderlord's Decree > Stormraider's Surge
I used to run Stormraider's on Fid to help me stick to enemies better after ulting in, but the speed buff is a little counterintuitive on a champ that's built on channeling abilities. TLD gives your combo a little extra trading power early game and a good combined burst with the runic echoes proc from your jungle item.
Sorcery > Fury
Obvious. You're a caster that should rarely be auto attacking unless farming camps.
Expose Weakness > Feast
See above for reasons why you don't take Fresh Blood. I like Expose Weakness over Feast as it makes your mid-late game teamfights that much stronger with buffed damage from allies. The massive AOE from Crowstorm (R) easily can proc this on the entire enemy team.
Natural Talent > Vampirism
Fid's drain is powered by AP, so the more raw AP you can fit into the build, the more HP you'll get back when draining. Vampirism is a little underwhelming, but go ahead and try it if you think it helps your survivability.
Any of these are probably fine. I like to take Double Edged Sword so that my damage is good whether I get the kills or donate them to the laners. Battle Trance really is more of a solid laning option rather than jungling in my opinion.
Most Fid players like to hit 3 and gank with all 3 spells right away. I usually will opt to clear my entire jungle first then go to gank so that I can farm them again afterwards. An early 2nd point in W gives faster clear speed and helps you get to the lanes to gank sooner. If you still gank at 3 with 2 points in W and one in E, just be ready to quickly level your Q mid gank so that you can cc the enemy asap.
This does of course open you up to level 2/3 invades though. If you want to be safer about it, go ahead and take a point in Q at level 3 instead. Typically I get early vision on the enemy jungler as well as some river protection with an early red ward so that I can get out of the way if something/someone nasty is coming my way until I'm ready to fight them.
Pots won't really help you since you're draining all the camps for HP. Start with 2 red wards and start playing the vision game as early as possible. Best early ward spots are on either side of mid lane in the small river bushes. Gives you a good idea of when mid is roaming and also lets you know if you're being invaded.
The build prioritizes shredding enemy squishies. The mpen from haunting guise and sorc shoes pretty much let you 1v1 gank any squishy champ.
Banshee's if you need a reliable way to dodge a single CC spell or if the enemy team has a ton of AP.
Zhonya's versus strong burst. Even works if they have no AD champs. VERY effective when you are the one initiating the fights.
Morello versus teams with strong healing. Pretty much your only option unfortunately to deal with healers/drain tanks/etc. Luckily you benefit a lot from the cdr and mana regen aspect either way.
Void staff versus heavy magic resist comps. Most of the time, I won't invest in this since it really isn't Fid's job to be dps-ing tanks anyway.
Rabadon's is good if you are the only magic dealer on your comp, as they likely won't itemize against you.
Finish Liandry's if your problem is massive HP-stacking tanks.