As per this site, I made a quick list using the Characters that are the only available characters to pass a certain obstacle.
Here is an overview:
Unique Character Abilities These obstacles can ONLY be passed by 1 character at the moment:
Starting out with these, you need to purchase 7 packs already. Those characters and the other characters/vehicles you get can also do more than just their unique ability however, and so you also have coverage for:
obstacles marked with (vb) mean that they can only be beating with a Vehicle Build from these 7 packs, I know its not ideal as you mentioned but it saves more money.
Cracked LEGO Ability (vb), Dig Ability (vb), Dive Ability, Electricity, Flight Dock Ability, Hacking Ability, Hazard Cleaner Ability, Laser Ability (vb), Silver LEGO Blowup (vb), Sonar Smash Ability (vb), Target Ability, Technology Ability, Tow Bar (vb), Tracking Ability, Vine Cut Ability, Water Spray.
That means you are still missing:
- Chi Power - (Cragger Fun Pack, Eris Fun Pack, or Laval Fun Pack)
- Drill - (Bane Fun Pack, Emmet Fun Pack)
- Fix-It Ability - (Doc Brown Fun Pack, Emmet Fun Pack, Jay Fun Pack, Nya Fun Pack)
- Mini Access Ability - (Bart Fun Pack, Gimli Fun Pack, Gollum Fun Pack, Slimer Fun Pack)
- Pole Vault - (Legolas Fun Pack, Sensei Wu Fun Pack)
- Spinjitzu - (LEGO Ninjago Team Pack, Jay Fun Pack, Lloyd Fun Pack, Nya Fun Pack, Sensei Wu Fun Pack, Zane Fun Pack)
- Time Travel Ability - (Back to the Future Level Pack, Doc Brown Fun Pack)
- X-Ray Vision- (Cyberman Fun Pack, Superman Fun Pack, Zane Fun Pack)
There are no easy ways to get most of these, there are a few people who have two:
Zane Fun Pack: Spinjitzu & X-Ray Vision
Doc Brown Fun Pack: Fix-It Ability & Time Travel Ability
Emmet Fun Pack: Drill & Fix-It Ability
Sensei Wu Fun Pack: Pole Vault & Spinjitzu
Jay Fun Pack: Fix-It Ability & Spinjitzu
Nya Fun Pack: Fix-It Ability & Spinjitzu
Based on this, I would have to recommend getting Zane and Doc Brown to cover 4 things, then the remaining 4, you'd have to buy individual packs for. Bringing the total packs to (7+2+4) = 13
This number will be greater if you want all the abilities to be unlocked via character and not vehicles, but can be lessened if you choose to use the in game "Hire-A-Hero" system by renting a character for 30 seconds using your in-game Studs to get the minikit for you.
Hopefully all this info helps, I'm at work and cant dig for links so I'll get links to the other sets up tonight and edit my post.