Hi there!
Just DL'd the game and I've got a solid idea of what yours will be like.
How I'll attack your project -
Analysis and plan:
Identify the Niche, the target audience, where we should focus our attention. Ie, One scenario may be that your game is far cuter and more colourful than 'Out of Line', and that you want it aimed at the 8-15 market.
Streams of traffic, free and paid. Free such as News, web presence, releases, evangelists, networking. Paid is completely up to your discretion, however I'm adapt at all things PPC and SEO.
Carrying out the plan, well, proof is in the pudding.
A/B testing, app store marketing. Let's see what descriptions and pictures give us the best results, compare them to other games in the area.
Geography. You say you want to attract a global audience, which is fine, but from experience it's always better to go deep and in one place with a strong market ( UK/NZ/AUS/USA ) rather than all of them in one go. It means we can gain traction among a group, which could then take off in the appstore, promoting organic growth. If we spread ourselves to thin, well, it could all be a bit of a wet towel.
Some of the apps I've worked/working on:
Nuklius
Whisk
OnePinkElephant
Other projects
Wallpark
Swoon editions
Please feel free to get in touch. Readily available from 06:00 till 23:30 GMT+0 every day.
~S