is it best to do a 10-15% water change every week or just a 25% water change once a month?

There is no generic volume that you should be doing, other than less than 50% at a time to avoid shocking the fish with a massive change in water chemistry.

As a rule, more frequent smaller changes are easier on the fish and more effective than larger volume less frequent water changes.

Your water tests will indicate if you need to do more frequent or larger volume changes, or both.

Start with weekly as that is a great schedule. Go for 25% a week, and then based on your water tests, increase or decrease the volume per week. If you end up needing 50% changes once a week, upgrade the tank and/or increase to daily water changes.

You must keep in mind the responses you are getting are just throwing random guesses out there, If your tank were to be 5 gallons, you may very well need to do more water changing, but if your tank were to be 50 gallons, you can likely do less. Other things such as filtration efficiency and your feeding routine will also impact the conditions.

Now it is up to you, but once the aquarium is cycled you can monitor yourself how your aquarium is doing by measuring your nitrAtes. The idea is that the water change routine will keep them relatively low - under 40 just before the next water change, and the lower the better. So now I would suggest starting off doing typical water changes of about 20 % per week and using nitrates as a reference so you can adjust your schedule according to results rather then blind guesses of strangers.

As the previous poster suggested, measuring nitrites and ammonia is useful on a tank not yet cycled, but on a fully cycled tank, which will have near 0 ammonia and nitrites even if it is neglected, it is nitrAtes we are measuring to monitor overall conditions.

Good luck.

If you have goldfish you need to be changing weekly you need to test your Ammonia and Nitrite weekly and depending on results it could be a 25% water change is enough or you might have to do 50% water changes

Freshwater needs to be changed MUCH more often than saltwater. Considering you have a goldfish, and they are dirty, you need to change your water AND vacuum the gravel 20% at least once a week.

10-15 every two weeks

25% a week with a gravel siphon