What are the best choices for a Bard/Rogue. I was thinking shield, Firebolt, and a utility cantrip.
Shield is a strong choice (pick from the Sorcerer list so that Firebolt is charisma based). It would be stronger if it wasn't so likely to make you wish you could cast it more than once a day, but those are the breaks. Absorb Elements is a similar spell to consider, it would likely get less use, but can save you from massive damage when you do need it.
You might not use the Firebolt often if you have Rogue levels since there is no way to get sneak attack with it, but if you are mainly a bard that might not matter. And whatever, flexibility is underrated by people theorycrafting optimal builds. Don't be a Bard/Rogue so you can be awesome at one or two or three things. Be a Bard/Rogue so you can be decent to great at nearly
everything. Firebolt it up.
If you are considering making your Rogue side an Arcane Trickster at some point then take it from the Wizard list so that you can eventually use it with spell slots. You'd be casting with INT for the firebolt though.
Other leading contenders:
Find Familiar: It's even better to get this through ritual caster since it is a ritual spell, but having a familiar to give you regular advantage (ie: the thing Rogues often need to do their job) is pretty sweet. Once again you have the INT casting issue with cantrips.
Something from the Druid or Cleric lists: so you can take Guidance as a cantrip: Because as a Bard/Rogue you are so close to being the greatest skill monkey ever to live, and this cantrip is the one easily acquired thing you are lacking. Unfortunately you would be casting with Wisdom, so you've got to take things where casting stat doesn't matter. Bless for Clerics and Goodberry for Druids are popular.
What subclasses were you considering?