The light fixture I removed has 3 white wires basically melted together. One black wire by itself, and the other two blacks are connected. How would I go about wiring a new fixture with one white and one black?
Do you have a photo from before the old fixture was removed fully? You need a hot plus a neutral for a light.
Likely the bare black wire is your hot switch lead, something you can verify with a non-contact circuit tracer (a tool you should own for safety sake, for example Klein NCVT-1). The white neutrals often get all tied together, don't worry about overthinking that one too much, just hook your white there.
The connected hots might be some totally other circuit using this box as a waypoint. Unless there are more lights run by the same switch, or something else, it's best to just ignore them and move on.