I recently spent 6 months in
Mexico using
wifi with no security problems. But pretty much the same as along the
California coast, with Marina and other paid services plus open relays. As already pointed out, as long as you use an https SSL secured website, there shouldn't be a problem. For
email, be sure that your webmail uses https and also does an encrypted signon-I am surprised to see that some still don't. Better is to get an SSL POP3/SMTP account (or 2) from Gmail, which are also encrypted. Better because with crappy wifi signals the lower bit rate than webmail is a real advantage. VPNs are the ultimate, but again, there will be a lot of times you want to communicate with marginal signals.
As far as what to use as a secure browser, I recommend
Google Chrome. Their architecture uses one process per tab, so wifi problems that occur with one tab do not close down the whole program (like they do with Opera, which I am using now).
And of course you need a good external wifi receiver. Many use an Engenius EUB-362ext or an Alfa (not the n version) as a USB adapter. You can move them outside on top of your
dodger for a good view, and they also accept an external
antenna. Lot's of others out there, but these are also
cheap. Anything beats a builtin
laptop antenna.
Have fun. BTW, there are also
internet cafes, but these range from good to dangerous, OK if you can bring your own
laptop.