Any ADO bus you take from Cancún International or Cancún City bus terminal to Chetumal or to Belize City should be safe and comfortable, in fact nicer than your airplane down. The bus will be fairly new, have reserved seats, there's a bathroom on board and a video player. The only downside is that most drivers put the A/C on Extra Cold.
Personally, if your schedule allows it, I'd bus to the Chetumal ADO terminal (less than US$25), a little over five hours from Cancún, take a taxi (around US$5 or less) to the Municipal Pier in Chetumal and take a water taxi (leaves around 3 pm) from there nonstop to San Pedro (around US$35-$40).
If your flight schedule puts you into Cancún in the evening, you could do the overnight ADO bus to Belize City and then water taxi to San Pedro. The bus company will help you through the border crossing into Belize -- it's usually no big deal.
Belize City is a little scarier for first-time visitors than Chetumal, but just take a taxi from what is called the Novelo's bus station to one of the water taxi terminals, US$4 or so. Relax -- most Belizeans you meet on the bus will be friendly and helpful and give you tips on what to do. There are three different water taxi companies that go to San Pedro from two different terminals on Front Street. Good info on transportation in Belize and Mexico on the Belize Bus Blog by a guy in Corozal who goes by Misterbee (just Google it), or in any up-to-date guidebook, such as the Fodor's guide I do -- a new edition is coming out in a couple of weeks.
Taxi drivers, bus ticket agents, border officials, etc. in Mexico usually don't speak a lot of English, but they're used to dealing with tourists and speak enough to handle most routine transactions, and some who have lived in the U.S. or studied English in school are fluent in it.
You might get hit with one or two extra "fees" that experienced travelers to this area might know how to avoid, but probably not, and even if you do it's not that big a deal.
Again, as you're really a tourist, there's no need for a customs broker, and, again, my advice would be to fly from the U.S. rather than deal with an airport in Tijuana or other border city in Mexico. And, even if it's a little more expensive, flying nonstop or at least direct to Belize City rather than through Cancún or Mexico City saves a lot of time and hassle.
If you plan to live in San Pedro, you should have a sizable bank account anyway.