Trace of iron isn't a number. It means the Culligan dealer used a poor test and can't provide a number.

You need to get a real water test from an independent lab before any treatment recommendation may be made. You want to know

pH
TDS
alkalinity
iron
manganese
hardness
sulfates
nitrates (if on a well)
bacteria

The big blue filter will do the same job as the sediment filter you have now - it will just last longer than you existing filter (assuming it is larger than the filter your are currently using).

For a relatively quick test to see what variety of iron you may have:

Fill a clear glass with tap water. Immediately look at the water. Is it clear or does it have some color? Are there any particles in the water?

Now leave the glass for an hour or so. Fill a separate clear glass with water. Is the water in the first glass as clear as the new glass, or is it slightly colored? place the glasses on white paper so you can see well enough to compare.