Star systems tend to only have a single economy type - i.e. they will only produce certain types of cargo. Sometimes you'll be able to deduce the economy type from the information on the main section of the galactic chart (ie. it may say "Imperial Industrial and Mining colony"), and in other cases from what it imports and exports.
As a general rule, systems based on agriculture will sell foodstuffs and other farm products cheaply, and will offer good prices for industrially produced goods. Industrial systems will sell manufactured products cheaply and pay good prices for agricultural products.
Essentially, the practice of trading between agricultural and industrial systems is the same as it was in Elite. However, whereas Elite only told you what type a system was (and you worked out what the best imports and exports were), First Encounters also tells you what the system's main imports and exports are. This greatly reduces the guesswork involved in identifying profitable trade routes, since you buy exported products and then take them to a system that imports them.
They will usually be offering twice the market price. Since this obviously makes you much more money, you should get into the habit of checking the bulletin board as soon as you land. Look for adverts reading like "WANTED: <product>. Will pay <price>". In some cases, there may be more than one buyer, and the price offered may be different. Always sell to the highest bidder.
The list of illegal goods can vary markedly from system to system. To a certain extent, the system's allegiance has a large effect on which products are prohibited. Each of the three main powers have their own laws, and in general all the systems in a particular power will usually have the same customs laws.
There are still variations from system to system, either due to local traditions or diplomatic agreements (the Imperial system Cemiess, for example, used to be a Federation colony and under the terms of the Emerald Treaty [check this] retains the original Federal customs laws). The systems of the Empire have the least variation in customs laws, although this has more to do with the fact that there are very few illegal goods in the Empire than a greater degree of central control. The Alliance of Independent Systems tends to have quite a lot of variation in customs laws, the most famous example being Gateway's tolerance of nerve gas.
Fortunately, it is possible to determine in advance what products are illegal in a particular system. After a trader successfully appealed a smuggling conviction on the grounds that there was no advanced warning on prohibited goods before entering a system, all galactic charts issued since 3180 have included a list of illegal goods in the system data.