If I could pick 3 pokemon, i would choose elekid, gligar, and kabuto, in that order.
Elekid is the only real sweeper of the 20 speeders, getting super effective hits on pretty much everything, able to avoid sucker punches from slower Croagunk and Houndour because of QA; it really does sweep teams, which is something that not a whole lot of pokemon can do. It is also the best revenge killer of non speed boosting Gligar, as Ice Punch OHKOs easily. Because of the prevalence of Gligar and other pokemon that Elekid outspeeds, Elekid is possibly the most useful pokemon in Little Cup.
Gligar is the best at the following things:
The best user of SD
The best user of Agility/Rock Polish
The best physical wall
The best baton passer
The best baton pass target
The best user of Stealth Rock
While a lot of this is debatable, it can do all of these things incredibly well. However, it can only do a couple of things in each set. This is a problem for both your opponent and you, as you cannot do everything with Gligar, so you have to choose four movess to put on your Gligar, and your opponent cannot possibly have a reasonable counter to everything.
Every team is Gligar weak in some way, whether it be a defensive team that loses to SD versions, or a team that is usually fine with Gligar, but when it passes +2 Speed and +2 Attack to Magby, now you've got another threat to deal with. weakness and Gligar can pass speed and attack to it. Many offensive teams are mostly beaten by the RP set, and physically offensive teams will have trouble getting past Gligar as a physical wall, even if they have Ice attacks, as Roost halves the amount of damage taken from them, as well as healing itself.
Gligar's only real downside is that since it reaches 19 speed, it speed ties with pretty much everything worth mentioning.
Now is when i give a shout out to Kabuto, who, with the correct support, can easily eliminate 2 to 3 members of the opposing team. Once rain is going, it's only real "counter" is Croagunk with Vacuum Wave, which is not uncommon, and why Kabuto isn't more used.
I would like to take a moment to point out how viable rain based teams are in LC, mainly because there is no Tyranitar to get rid of rain, and the only weather changers are easily taken care of by Kabuto. Hippopotas and Snover are still outsped when it's hailing. Snover, if it isn't KOed, will at least take a large chunk of damage from Kabuto's Rock Slide, and Hippopotas will be OHKOed by Waterfall. In the rain, Waterfall is a OHKO on Gligar and Misdreavus, the two most common pokemon in Little Cup, assuming Stealth Rock is in play. If you can catch Croagunk on the switch-in, Rock Slide is a OHKO (I believe).
Throughout all of this, I haven't said a word about Kabuto's greatest asset, STAB priority that is boosted in the rain: Aqua Jet. Anybody who know anything at all about Little Cup will tell you just how important it is to have a fair amount of powerful priority attacks on a team. Aqua Jet and Swift Swim allow Kabuto to get the first attack on your opponent almost always, and has the attack to back it up.
The only downside of Kabuto is that if the rain stops, it's speed drops and its a bit of a sitting duck.
So there's my 2 cents, I voted Elekid, if anyone is wondering, because in today's metagame, it's the most useful sweeper in LC.