Well, I figured it out and kept my people fairly happy during the first mission of the campaign, though I kept sinking into debt near the end of each year (I was trying to use logging camps to export, since the actual bananas did nothing for me when people kept eating them).
It crashed upon autosaving, though, which frustrated me enough to turn it off for the night.
Logging camps on their own are pretty useless when it comes to cashflow, as logs are one of the most low-priced exports of all. However, lumber and furniture aren't, so if you decide to go this path, get a lumber mill, and eventually, a furniture factory to supplement the logging camp(s). Be sure to upgrade your logging camp so as to provide a nice production boost as well as not having to rebuild the logging camp nearer to the actual trees all the time.
As mentioned, mines is your best bet of getting a good, solid foundation to build your economy on, as mines are relatively cheap, and because minerals have very high export prices. Gold is a very lucrative export, especially if paired with a jewelry factory, but iron or bauxite is sufficient if the gold is too far away (or on some islands, lacking all together). Though remember to back it up with another industry in a decade or two, as mineral deposits are not infinite.
Tobacco and sugar are also nice exports, and also the cheapest to set up, just pop a farm or two at sufficiently fertile ground and you're good to go. Though you should eventually upgrade it with a cigar factory (if you're growing tobacco), or a rum distillery (if you're growing sugar). Just remember to not enable the Prohibition edict if you go with the latter, as it will shut it down.