Alright so this may not seem helpful, but. Jungling is all about flexing to the needs of the moment. You need to be able to project where the game will be, at least 1 minute in advance. Then position yourself to be ready to gank a lane at that time. ** Also, never underestimate the major jungle objectives.** If your top lane has pushed to the enemies turret,** TAKE. HERALD**. It's easy money, the buff is useful for the top laner, and Herald is generally overlooked as much as Baron.
If one of your lanes, such as top or mid need to recall and they are being pushed, then cover their lane. If the minions are going to go to turret, you might as well get exp from them, and maybe even some gold. HOWEVER, do NOT push their lane. Only last hit until they are back, and generally don't spend too long in top lane. The reason for this are the following, top lane is the farthest from bot lane, AND dragon. If you are top for too long, it leaves bot lane open to enemy jungler ganks, and dragon open to be taken by the enemy without you to contest with your smite. On the same coin, if the enemy jungler is top lane, gank bot then try for dragon. You also almost always want to go for dragon if the enemy jungler dies, as it is for the most part, a free objective/gold/buff for your entire team. Which if you haven't gotten the point already, DRAGON! DRAGON! DRAGON! This is a crucial objective that should be kept control of.
If the enemy team has a Twitch/Shaco/Teemo/Akali smiting the birds is the last remaining oracles effect in League, if you are about to gank an akali, ALWAYS smite birds before hand, it will make her smoke screen/invisibility worthless. Not to mention its use for clearing wards to set up a bot/mid lane gank. and speaking of birds don't clear them if you can kill the dragon Snail Crab/Snugglebutt/Puny Peasant/Rift Scuttler. Speaking of scuttle, if your champion has no hard CC, smite the Gromps/Rocks for the ability to stun, stunning the Scuttlecrab will give it -10 armor and MR, making it massively easier to kill.
If you're higher elo, and your team is doing well, do NOT be afraid to try for a 20 minute baron. This is one of the most unexpected plays you can make in the jungle roll, and since it JUST spawned, NO ONE expects it. If you want to try for this play, make sure you take the scuttle crab about a minute before it spawns, and have your team take the path above blue buff if you are blue team, and below red buff if you are red team. This is to hopefully avoid any wards that may be around the area, if you are suspicious have your support go first with a sweeper to check it out. The reason why this works so well is because no one wards baron that early, but if you get caught by a stray ward off in the side, you're boned.
If bot or mid lane are doing well, don't hesitate to give up your buffs. It's easy to be selfish and horde them as a jungler. But if you can bear the pain of actually having to recall once and a while, then let your mid have blue buff, and your ADC red buff. Their success because of you handing a buff to them, will allow you to have an effect on other lanes while you're farming or ganking more isolated lanes, such as a struggling top lane.
I would not recommend counter jungling, or at least until you're more experienced with your own jungling. And because of this, I don't recommend junglers that are best suited for counter jungling, such as Shaco, Nunu, or Aatrox. The main issue is that you don't want to counter jungle without proper vision. And unless you KNOW where their jungler is, it's not worth the risk most of the time. Counter jungling effectively is the highest mechanic in jungling, and playing it well is the equivalent of playing a Vayne with really good mechanics.
Obviously jungle path is versatile and will change to fit your needs within a game. But here are some videos that show optimal jungle pathing for farming. Whether it's farming for gold, or farming for devourer this will help your optimal clear for maximized efficiency. I will link a few other videos that will help you a lot, and sorry for the wall of text.
Highly Recommended How to effectively clear jungle camps: https://www.youtube.com/watch?v=3nhNrIjbYmM
Amazing jungle guide for almost all jungle champion: https://www.youtube.com/watch?v=wo4u5RSAHt4
Effective Farming clear: https://www.youtube.com/watch?v=oECw20l6TGI
I hope I helped, good luck on the Rift!