American is part of the One World Alliance.
Here and
here are articles on redeeming miles for awards in this alliance. Check out American's website, look for route maps and charts for how many miles it takes to get there. British Airways is a partner but charges large fuel surcharges. LAN has lots of routes to South America and has lower fees on award tickets. I flew to Rome on AA for 40,000 miles and $50 in May (off peak award).
United is part of the Star Alliance.
Here and
here are articles on using miles on Star Alliance carriers. United's biggest partners are US Airways and Lufthansa.
Here and
here are articles on the best hotel credit cards. Which one is best for you will depend on where you want to go and what hotels are there.