It depends if you have access to a flow cytometer. If you do not have access or if it is costly, the best option could be the SCD test (Halosperm and such), or maybe the Comet (not sure about the costs, best checking a recent article and calculating reagent costs). For the Comet, you need electrophoresis equipment too. In both cases, you need a fluorescence microscope, but SCD can be performed with a cheap light microscope.
TUNEL can be used with fluorescence microscopy, but reagents are typically expensive.
If you have cheap access to cytometry, then SCSA is the cheapest option, but you have to standardize it very well. TUNEL can be used with cytometry, but it is ranges of magnitude more expensive.
Regarding cost-effectiveness, it depends on your objectives. Different tests will provide different information. Moreover, microscopy tests require more work than cytometry (you have to manually count lots of spermatozoa; if you want more speed/objectivity you have to resort to automated or semi-automated methods, which are also more expensive).
Felipe Martínez-Pastor gave a great answer regarding the methods to assess DNA fragmentation. The problem regarding cost effectiveness is that there is no good evidence and data about the clinical application of the method since even using ICSI you can not tell which sperm has a fragmented DNA as there is no visible morphological sign for DNA fragmantation