These Pokemon (including the evolution line) can learn "Sticky Web"
Ariados, Shuckle, Surskit, Kricketune, Sewaddle, and Galvantula
Sticky Web is one of those strategic-use moves that you would want to go first ; such as Stealth Rock, Toxic Spikes, etc.. So, you want a Pokemon with incredible speed.
Right off the bat, it's Galvantula. Galvantula has the second highest base stat total based on these. Not, only will he provide this move fast, you can support him with some STAB - special attack moves too. Honestly, I think he'll be a great Pokemon for you. Also, even though he has low defenses, he has minimal weakness too - fire and rock ; 2/18. This will definitely be helpful.
Your next option is shuckle. Now, you're probably thinking, why should a have a slow Pokemon like him. Well, there are two reasons:
1) His defense. The chances of knocking out shuckle in one shot is pretty low. You would have a good chance to use this move.
2) In double/triple battles, you can have a support Pokemon who knows "Trick Room". Therefore, your shuckle would be the fastest for 5 turns, and you can use any move you want. Some fast Pokemon that can learn this are mismagius, espeon, etc.. Or, you can have a Pokemon like Dusknoir who's slow - but using trick room would make both Pokemon great sweepers and a great team.
Both are great choices for you! ; Then again it is up to you! Hope I helped! :)