UA miles are good for CO, they're both in Star Alliance. So if on CO you see the flight you want, call UA and demand it.

As per getting miles quick just do the best promos for each card as they come up until you've eventually gotten (and cancelled) them all. There's an easy fee-waived 500K or so in promos floating now that may have to be spaced out over 2-4 months.

After you've done all the best promos and can't churn much, settle on one or two low fee or free cards for all purchases, balance paid in full automatically each month from your checking. (You also get a month's float on life this way). SPG ($65) and Fidelity AmEx (no fee- 2 Air Canada miles per $1 spent) are peoples usual favorites for everyday spending.

And don't be timid about including some dollar coins in your spending.