One of the paladin spells is Find Steed, which summons a spirit taking the form of a steed. Can it carry my party's stuff, like a regular animal can?
It is just another creature, and creatures can carry things. It doesn't come with anything other than itself when you summon it, so if you want anything else, you'll need to buy it and put it on yourself.
As for specific carrying capacity, please see the stat block for the creature and the rules on lifting and carrying.
My table allowed the steed to generally carry certain things even when dismissed.
We generally hand wave a lot of the mount rules to simplify control and management at the table (acts on players turn and is fully controlled by player.) There are times when the DM stepped in to say "NO" to some things, but that's about it.
In terms of items, I worked with my DM to determine what it would "always-have" and what it wouldn't. Once agreed, it was agreed and we just moved forward.