You'll certainly want to do both. Early on you'll need a little bit of everything so you can equip everything you need. Keep every crew member and crew components (the medium slot stat boosters) you find. When I play I reserve the first 4 slots of my main cargo bay for consumables and fill out the rest of the main cargo bay with crew, while I keep crew components in my ship stash.
You only need to equip them in 3 circumstances:
1.When you need to equip an item you do not have the base stats for. Most items will still function even if you lose the required stats after it is equipped.
2. You'll need to level up your crew to keep them relevant. You level them by killing enemies while they are equipped (they do not get experience from completing quests).
3.When you don't have the base stats to use an item that has to be activated (things like weapons, computer active boosts, etc.). Any item that requires you to press a button to use it requires you have the minimum stat to use it.You typically won't be doing this until late game when you can afford to start dumping all of your stats into command.
Other advice I can give is do not worry about always equipping the best weapons. It's often better to not continuously upgrade because the energy usage of new weapons quickly outstrips your ability to restore/maintain your energy pool. That said do not let it fall behind or you won't kill anything either.
Hope this helps.