@pwsteele, with verbs of movement such as ir/vir, the preposition para is optional when you’re stating the purpose of the movement, and only mandatory (etiher para or a) when you’re stating the destination:
- Nós fomos a Sintra (para) visitar o palácio
- Eles vieram para Portugal (para) viajar
Between a or para, as in your last two examples, it’s largely up to the speaker’s preference, depending on how they perceive or want to express the duration of the movement (although sometimes, people use them apparently indiscriminately). Here’s a useful forum topic about that: “A” or “para” with verbs of motion? - Portuguese Questions / Grammar - Practice Portuguese
Basically, a usually suggests a shorter stay than para.