I'd definitely recommend wrapping outside in.
If you start at the inside, each subsequent turn of tape has its upper edge (as you approach the brake hoods) over the top of the previous one, and it's this upper edge that will tend to ruck up under your hands as your weight tends to push it forwards and downwards. If you use tape that has lots of adhesive on it, and wrap it very tightly, this effect can be minimised, but then on warm days the adhesive tends to ooze out and make everything gummy, and if you wrap padded tape very tightly, you're squishing the padding, reducing its effect.
If you start at the outside, there's less tendency to ruck up under your hands' forward pressure, and you don't need to wrap so tightly. You do have to secure the ends at the centre of the handlebar, but you can do that quite neatly with good-quality electrical insulting tape.
To do this, trim the inner end of the bar tape diagonally so that it ends flush with the edge of the last un-trimmed wrap. Then use a single wrap of insulting tape, half over the bar tape's last wrap, and half over the naked handlebar, pulling it tight so that it stretches to take up the thickness of the bar tape. Leave the end of the insulting tape underneath the bars, where it's less visible.
Good quality insulting tape will stretch in this way, and the adhesive will stay put for years - probably longer than your bar tape will last. The cheap stuff doesn't stretch and doesn't stay put, or goes gooey. You can even buy it in a colour to match your bar tape. Or your frame. Or eyes - whatever you want, really.
For touring, I also highly recommend the gel pads you can put in under the bar tape - subtle cushioning that's well worth-while.
My favourite touring bike has Brooks leather bar tape, with Specialized "Bar Phat" gel pads under it, wrapped in the way I've described. It's comfy, and looks like out-lasting me. It fades in the sun, but it's been on there maybe ten years so far, coping with Irish rain and South African sun and still going strong after thousands of miles.