I was taught that one can use the '-que' suffix to string together multiple words, in a similar way to putting 'et' between them.
Are these two equivalent? Did one have a connotation in classical (Caesar-era) Latin that the other didn't?
The way I was taught was that, as a general rule, -que is used:
So, consider the example of an opening line from Catullus:
Lugete, o Veneres Cupidinesque
Venus and Cupid have a parent-child relationship, and so the -que makes sense.
Compare this to the opening paragraph of De Bellico Gallico:
Gallos ab Aquitanis Garumna flumen, a Belgis Matrona et Sequana dividit.
The Marne and the Seine are just two out of many rivers, so
et is more appropriate.
That being said, this is not a hard and fast rule. You have for example in the opening chapters of Augustine's Confessions:
et quomodo invocabo deum meum, deum et dominum meum (1.2.2)
deus es dominusque omnium quae creasti (1.6.9)
So, the same author, using the same words just paragraphs apart, uses both et and -que.
In Ecclesiastical Latin "-que" would be used in order to avoid to much repetition of the use of "et" and for drawing similarities to the original first noun in a statement, as is sometimes found various Litaniae Sanctorum.
Sancti Petri et Pauli, atque Andrea, ora pro nobis.
In this phrase we can see a similarity between Peter and Paul (Apostles of Rome) and yet at the same time another similarity between Peter and Andrew (brothers).
Both et and -que can often translate "and". The use of -que is more limited (see James's answer), so et is a safer choice.
The suffix -que only means "and", but et can also be used as an adverb ("also", "in addition"). Sometimes et and etiam are both equally valid. As a rule of thumb, you can use et whenever you want to add something. Sometimes etiam or quoque is better, though.
James Kingsbery's answer is exactly correct. If two things "belong" together, then -que is appropriate. If you were going shopping, you might be asked to pick up ova butyrumque ("eggs and butter"), but if you were talking about what you saw on your walk through the countryside you'd be more likely to talk about boves et rusticos ("cows and peasants").
The que suffix has a usage example with momentous consequence. Filioque was inserted into the Nicene creed in the West sometime in the Middle Ages. The result was
“... qui ex Patre Filioque procedat”
Making the Spirit proceed from both the father and son. This is one of the few theological controversies between the Catholic and Eastern churches.
Although this is medieval, not classical, the relatedness of Father and Son is emphasized by not using et. Two persons cannot be more closely related than being of one substance or being.