Evan,
Been doing it manually for months? Well model builder is the way forward! It's the next step for non-programmers to become "power users". Clearly the light bulb above your head has popped on for you. I would seriously consider asking your employers to put you through a model builder training course, it's for their benefit too as you'll be working faster and smarter automating your workflow rather than doing it manually ....for months....
That said, those "error" messages about indexing are not errors they are warnings as indexed fields perform better in joins.
You said:
I want to join a table to a point layer and then select polygons that contain the matching records.
In your model you show you are using a Select Layer by Location, if you are selecting by location why are you either doing a join, the result of the join (in your model) has no outcome on the spatial selection. So I wonder if when you say "...select polygons that contain the matching records" your are really meaning when field XYZ in the joined table has the same value as the field ABC in the polygon layer? If that is the case you want to by using the Select layer by Attribute tool.
As Dan hints the way to turn a model into a generic tool is to expose the inputs/outputs as parameters this would allow a user to select any table but you would need to expose the other parameters too so allow them to choose the correct join fields.
Get yourself on a course and stop doing things manually for months!
