To the OP, if you do not speak Portguese then traveling outside of the main cities will be a problem without a guide. Spanish would do you know no good.

While Miami is a hectic airport it is more or less a good halfway point between LA and Brasil although the MIA/GIG leg will be about 8.5 hours. If you fly AA I would suggest buying a day pass at the AA Admirals Club that you can use at LAX and then at MIA. At MIA you would have a chance to shower and change which is a godsend when traveling long distances. On the return, if you fly out of GIG and buy another day pass you can shower and change at GIG before leaving (good idea since you will likely check out of your hotel in the morning but flights back to the US leave late at night).

There are many very dangerous parts to Rio and in crime is much worse than the US even in tourist areas. I suggest you spend some time reading threads here on FT or elsewhere. You will also need to get a Visa ahead of time before traveling to Brasil (cost is $180 I think now but good for ten years). There are no airport Visas.