1. Wendy's the best Adventure mode character on the whole, I think, because she can make a long-term sustainable camp in some downright godawful conditions, and Adventure Mode is all about putting you in terrible situations. She's also an absolute beast in the final stage, because every perk she has is constantly operating at full power in it. WX-78 is also a contender for being the best if you're willing to intentionally kill yourself until you get "The Game is Afoot" as your starter scenario, otherwise his poor starting stats and vulnerability to precipitation will really make him struggle. Willow's got Sanity issues but her lighter is a really good fallback for the final scenario. Wolfgang's awful, because he relies heavily on having a well-established food production pipeline which you'll never have the opportunity to set up. Wilson and Wickerbottom are okay, and I've never used Woodie in Adventure Mode but it seems like he'd be a solid choice in theory, since he could blitz difficult areas in werebeaver form. The other two characters are the entire reason you're playing Adventure Mode in the first place, so I assume you don't have them.
2. Pick one scenario to build yourself up in, but otherwise try to complete scenarios within 30 days or so. You retain all of your invention knowledge from one scenario to the next and get to choose 4 items to bring with you each time you complete a chapter. A Cold Reception and The Game is Afoot are probably the two best suited to build up in, but Archipelago will work in a pinch. Don't try to build up in The King of Winter. It won't end well. Just get the hell out of there as quickly as you can.
3. Invent as much as you can in your build-up scenario, and try to hunt the MacTusks to get a Tam o'Shanter and Walking Cane. Build a Lantern. Take the Tam o' Shanter, Walking Cane, and Lantern with you from world to world. You'll understand what the Lantern is for when you reach the end.
4. The final stage is perpetually night time. That means constant Sanity drain and instant death if you're caught without a light source at any time. This is where Wendy and WX-78 shine. Wendy loses 25% less Sanity to darkness and Abigail is at full power at night. WX-78 has across-the-board excellent stats at this point and should have a stockpile of Gears carried over through the scenarios to eat to maintain his Health, Sanity, and Hunger.