SaintVicious, jungler for the CLG.NA team, once said it on stream. If you are certain that you are not going to be counterjungled, then sure, smite right away. However, circumstances can quickly change while you are attacking the creep (assuming smite is used on objectives like buffs).
Situation #1: You are jungling but leave base a little late. Like usual you head to Red and you feel confident so tell your team you don't need their help leashing it. So you smite right away and begin autoattacking it. In the animation of your last auto-attack, the enemy jungler smites it away from you over the wall, then turns and kills you with the help of the small lizards and the red buff they now have cuz your smite was down.
Situation #2: You have been jungling and cleared the jungle already. As typical, you get ready to feed your AP Carry the blue buff. While, waiting for the AP Carry to deal the finishing blow, the whole enemy team comes charging from river to the Blue led by their jungler. Fortunately this time, you saved your smite, so before the enemy jungler can smite steal it, you secure blue for your team. While not optimal, certainly better than the enemy team having both blue buffs.
Finally, it is good practice as it helps you use smite to secure important objectives like dragon and baron. After all practice makes perfect, and if you say that you always use smite first except for dragon and baron, you won't be as practiced. A few seconds lost on the smite cooldown is hardly noticeable most of the time, but gaining a little more practice on using your smite to secure kills never hurts anyone.
This strongly depends on the match-up and how well you're doing. If you're against someone who you can trade against easily and always come out on top in said trades getting a Dorans will generally be a better idea because it'll improve your damage more than low level alternatives. This is generally true if you're playing a champion that hits harder versus a more tanky champion that doesn't deal as much damage. Say Riven versus Cho'gath for an example, Riven would probably want to grab x2 Dorans before going into her build to give her more damage potential on Cho'gath since she normally comes out on the good side of trades.
Alternatively, if you're getting bullied pretty badly you can always go for Dorans items (they're fairly gold efficient), though I'd probably recommend getting a Wriggles because of higher sustain and the damage reduction. A lot of top lane is knowing your preferred champion's match-ups and how well he/she trades against their enemy in lane.
For a little bit a math on Dorans Vs Wriggles I'm gonna add a link to another answer on here. Just for Context: The question is about Dorans Vs Wriggles on an AD carry, but the math still applies universally. https://gaming.stackexchange.com/a/59537/7494
Additionally, if you get fed early and can afford beefier items you should almost always go for those, but getting Tier 2 Boots, x2 Dorans, and a cheap defense item at low levels will almost always be better than trying to save for a 1.5k+ gold item early.
Hope this helps :)
Best Answer
I used to play dota for 8 years and I ve been playing LoL for a year now.
History of the skill
The skill you talk about was at first developed by DotA players. In DotA, cancelling the post shot animation helped you in shooting a little faster - for an unskilled eye almost unnoticable. It helped mainly when you had a hero with orb skill like frozen arrow (drow ranger) or fire arrow (bone fletcher) and thus it was called orb walking. Players of LoL no longer calls that orb walking and therefore we can say there is no such a thing as orb walking in LoL, but because I am an old DotA player, I will dare to call it orb walking in the text below.
Keeping range
As Lyrion and Rakesh Reddy say, you gain time to keep your distance between you and your target, so basically you will not get out of your attacking range and you will not lose vision. That is pretty important.
Keeping your character in motion
Another advantage is that you keep your character moving, which makes you harder to hit with any skill shot:
Positioning in a fight
Last but not least important is the fact, that you position your self in the fight, which is what range ad carry really has to do. In order to win a fight, you always have to maintain secure position where you can shoot and dont get shot / focused. For instance:
You can shoot your enemy and meanwhile walk in a brush nearby giving you ultimate position for finishing your intensions (killing, harrasing, switch from harrasing to farming).
Practising "orb walking"
If you want to practice orb walking, the best way to do it is to do it a lot. Doing it poorly in a game will cost you last-hits and positioning, so treat it initially like learning a new champion. Do it in Custom or AI games, then normal games, then bust your new skills out in ranked. I recommend starting by doing "laps" around a creep-wave with it. Just circle the wave and auto-attack (don't worry directly about last hitting), but move between auto-attacks. Once it's clear, find the next wave and repeat. When a wave gets to turret, you can do the same thing around the turret. This is a mechanical skill, and has a little variety between champions (in terms of when/how fast to cancel), so requires a great deal of practice to get absolutely correct.