Is a player required to spend their XP, Influence and/or Credits during the upgrade phase of a campaign or can they bank it for later?

They can bank it. In fact, it's often wise to do so. What I often do is look ahead at what the ideal upgrades will be (for spending xp), so that I don't waste my current xp on sub-optimal choices. IMHO, it's often worthwhile to get a couple of 1xp or 2xp abilities and then save up for one of the bigger ones (3 or 4 xp) after that. That's what we did in Descent 2.0 and it made a big difference.

Same thing for purchasing. Nothing is more of a let-down than to draw the ideal item for your group to purchase, only to realize that you're 100 credits/gold short.

yeah, I agree with thereisnotry. as the rebel player, getting a couple 1-2 xp cost skills can make the early missions much easier. the commando allowing someone to move 2 squares at the start of his activation can pull someone out of danger or set someone up for a decisive action.

the smuggler ability to move 1 square every time an attack is resolved against her can be very life-saving; and the wookie being able to strain himself to heal 2 HP may not sound like much, but it can make him that much more tanky. but mostly, the rebel players need to discuss which upgrades each of their characters should take to better synergize with each other.