This is interesting.
As for the all time best, it really depends on how we're defining best. If it's the best wrestler who happened to win a Royal Rumble, then it's Hulk Hogan, bar none. Most of the all time greats have a Rumble win, but really, none of them stack up to Hogan. Hogan didn't win when it was good for a title shot, but it didn't particularly matter, since he was WWF Champion in the first win, and went on to main event WrestleMania in a loss to Warrior, and in the second he went on to challenge Sgt. Slaughter for the title and recapture it at Mania.
If you want to go with the person who took the best advantage of their title shot, well, it's kind of a wide field. A large number of guys who've won the match have gone on to win the title - Yokozuna, Bret Hart, HBK, Austin, Triple H, Lesnar, and potentially more I'm forgetting about. Based on this particular criteria, I would have to go with either HBK or Austin, for their 1996 and 2001 performances, respectively. Shawn because he went on to have the Iron Man Match at WrestleMania 12, which I personally really enjoyed, but many nowadays dislike. Regardless, it's one of the most important moments in wrestling history when Shawn wins the title. I go with Austin in 2001 for the X-Seven match, which saw him pull off the heel turn that was rather stunning (no pun intended) and another very important moment in history. I'd go with Shawn, but that's not really how I'd judge it.
My personal criteria is the person with the best Rumble performance, then it comes down to three men, in my opinion, and I'll choose one in a moment. Shawn Michaels and Chris Benoit are the obvious candidates, having entered the Rumble at #1 and winning it, the only men to do so. Shawn's, however, has something of an asterisk on it, as the entrances were timed a minute apart, rather than two - making it one of, if not the, shortest Rumbles ever (the original might have been shorter, as it was only 20 men - not quite sure). Benoit is tied with Mysterio for the longest Rumble appearance ever, and though WWE claims Mysterio's is longer, they clearly won't acknowledge Benoit's time, so they might be wrong. Still, a #1 appearance and very impressive.
I believe, however, that Ric Flair's 1992 appearance was the best ever. This was, to date, the longest Rumble appearance at 60 minutes, and should be something like #5 overall. He entered at #3 and outlasted everyone else to win, and I think it's the most impressive overall performance, for several reasons. For one, Bobby Heenan's commentary is absolutely fantastic throughout the whole match. He's got money on Flair and is also a personal supporter, and he's constantly throughout the entire match talking about Flair, putting Flair over, reminding us that it's not "Fair to Flair". This commentary combined with Flair's top notch selling, and getting his ass kicked all over the ring, by damn near everyone, makes Flair look like he's just taken the worst beating of all time, for an hour, and outlasted everyone to win the title. Heenan did his job so damn well that even though Flair was a heel, you were cheering for him. Heenan's commentary, Flair's performance and selling, combine to make Flair's performance just amazing. I watched this match 16 years after the fact, a few months ago, and marked out for Flair when he won. I can't imagine what it was like when it was live.
So, as for the best all time Royal Rumble winner, I go with Flair. Now, the worst?
I'll run through the same criteria. If we want the worst wrestler who happened to win a Rumble, it would have to be Yokozuna. Zuna was impressive for a short time as being so damn enormous, but he was really a poor wrestler at the end of the day.
For the wrestler who used the Rumble win to the least advantage, it comes down to our last two winners, I think. Cena pretty much ruined it all by taking his opportunity at No Way Out, instead of having the Cena vs Orton that was clearly brewing as a Mania main event. Potentially even worse, however, was Orton. Orton won the Rumble, and then barely talked about it. He acknowledged it like, twice, and that was only to save his career. He then went on to have an uninspiring performance at Mania that was really just a let down after the awesome build up they did for it. I still maintain that they should have turned the match no DQ and had Vince turn on HHH to cost him the title and thus join Legacy, but I digress. Really, I go with Orton here, as his Road to WrestleMania barely mentioned the Rumble at all, and his WrestleMania performance was very lacking.
The worst overall performance could very well go to Orton as well, who really just didn't do anything special. It was only a few months ago and I can't even particularly remember anything notable out of it. I can think back and remember a Yokozuna, who was dominant and then threw Savage over the ropes with a kick out, or the Austin "no referee saw me, I'll just head back in" spot, or HBK keeping one foot up and then superkicking Bulldog over the ropes. I honestly can't remember Orton doing anything that great except throwing HHH over the ropes while he was yelling about something, and that's hardly memorable.
Based off the last two I've just listed, I'd say Orton is the worst Rumble winner of all time. His performance was forgettable, his path to Mania barely acknowledged it, and at Mania he was subpar. Orton might be a good wrestler otherwise, but as a Rumble winner, he failed.