Old house - hanging a new light fixture
Rule # 1 - When making a replacement, don't touch anything else.
In this case, that means you only use the wires connected to the old fixture - white (neutral) and red (switched hot). Ignore the other white wires and the black wires.
Rule # 2 - In the US, Hot/Switched Hot can be ANY color except white (neutral), gray (neutral), green (ground), bare wire (ground).
In this case, that means red == black.
Rule # 3 - All grounds go together and can include metal boxes &amp; conduit.
This one is a little tricky. If there are no ground wires then that should mean that your metal junction box is connected to metal conduit all the way back to the panel. If that's the case then you can ground the new fixture using a grounding screw.
The big question, of course, is whether or not the metal box is truly grounded. If you see metal conduit &quot;everywhere&quot; then that is a very good sign. If not, there are ways to test (essentially, if everything is wired correctly then &quot;ground&quot; == &quot;metal box&quot; to &quot;hot&quot; should read ~ 120V and &quot;ground&quot; == &quot;metal box&quot; to &quot;neutral&quot; should be almost no resistance).
End result:

White (new fixture) =&gt; white (ceiling)
Black (new fixture) =&gt; red (ceiling)
Bare ground (new fixture) =&gt; green/bare ground or metal box (ceiling)