Excellent idea. I will edit this post with my answer when I think of it. Needs a lot of thinking. Mostly modern players, as I said...don't know too much about fielding skills of the older guys except from legends and folklore.
EDITED - WITH MY FIELDING TEAM
Keeper - A tough spot. I mean, you got guys like Ian Healy, Adam Gilchrist, Kumar Sangakarra, MS Dhoni...even Rahul Dravid (note: not a keeper) did an excellent job behind the sutmps for india for years. But I would say that my keeper spot goes to Mark Boucher. You don't get 1000...and I'm giving him the thousand...international dismissals by being a slouch behind the stumps. While not the most graceful of keepers at times, he is one that few would doubt deserves this spot.
1st slip - It's actually very different from second slip. First slip is, I think, a bit tougher. You have to have an excellent relationship with your keeper on which balls he will go for and which you will go for. It's hard for a first slip to not dive for a chance, only to see the keeper grass it. But first slip stands ahead of the keeper, second slip usually stands in line with the keeper. If he dives, it puts a huge blind spot in front of the keeper. So if he dives, he had better take that catch. Plus, the unwritten rule is if the ball goes between first slip and the keeper, it's the keeper's catch. But cricket isn't that easy. If the ball goes between them and is dying...first slip has a better chance of catching it, doesn't he? That's where the understanding had to come into play. As I mentioned before, any number of men can easily slot into a slip fielding position and be called great. In my few minutes of research I've seen several who many have called "the best". But in keeping with the theme of guys I have actually seen, I would have to go with Stephen Fleming. A man with one of the best cricketing brains of all time, and an excellent fielder to boot. He would definitely have that communication with his keeper on which ones to go for and which ones to leave.
2nd slip - Oh, come on. Brian Lara. He had the safest pair of hands in the slip cordon I've seen in my time.
Gully - I would put Paul Collingwood at gully. More of a fine gully, quite backward of point if you want to call it that. But nothing would ever pass him for sure.
Point - No thinking here. Jonty Rhodes. Enough said.
Cover - AB de Villiers. As I mentioned before, the area between backward point and cover is usually filled with excellent fielders. For good reason, too. The cover drive is the epitome of an excellent shot for a batsman, and therefore cover and point (for the mistimed drive) must be well protected. The cut shot and square drive also hold very high regard, so you need an excellent backward point as well.
Mid off/mid on - It's almost the same position, with the one difference being that mid on is more likely to have a ball in their direction due to the off drive being very difficult to pull off properly and the prevalence of most batsmen to play to the on side these days. You never really see specialist mid off and mid on fielders in the modern game. In Tests it's usually a fast bowler in one of those spots, to offer advice to whoever is bowling. In the other spot it's usually a man who isn't particularly the best fielder (Daren Bravo, I'm looking at you) or the captain himself. But this is a topic about the BEST, so I'd want two guys with good, safe hands in both positions who are also accurate enough with their returns to possible effect a run out from a quick single. I'd give Mark Waugh mid on and Dwayne Bravo mid off. Both have excellent and safe hands, but since mid on would have more action, I'd give Waugh that spot as he would fire in a return to the MAN at the stumps rather than the stumps unless he has to. Bravo would immediately throw at the stumps rather than the man there. Sometimes he would hit, sometimes he won't. And when he doesn't, there will be overthrows more likely than not.
Short leg - Ricky Ponting. No doubt about that. I have never seen someone else in the modern game volunteer themselves for that spot, save for Ramnaresh Sarwan. Both men actually WANT to be right under the bat, and they're both very good at it. Why I would pick Ponting over Sarwan is that he stays down until the absolute last moment. The batsman is practically through his shot by the time Ponting decides to start coming up. Sarwan stays low for a long time himself, but he often takes evasive action too early. As I said before, Ponting isn't afraid of wearing a few bruises for his team.
Deep square leg - The guy here needs to be able to be quick across the ground and also have an excellent arm to send the ball in from the deep. He must also have a decent catching ability in the case of a miscued hook or pull. Again, you don't see very many specialist deep fielders these days, and this would be a very weird choice, but I would put Tillakaratne Dilshan at deep square leg. He is an excellent run-stopping/short fielder in his own right, but in the deep he is just as effective and he would be excellent at this spot with his safe hands and strong arm.
Next question is who is going to bowl to this field? I'd say Malcolm Marshall, but he needs about 2 more slips, another gully, a short backward square, silly point, and a batsman with no fear.