In sending letters to your Congress-persons (!), I recommend you reference the annual report the FBI presents to Congress concerning crime in the United States. That report provides a lot of statistics, one of which is that assault weapons are used in less than 1% of crimes. Therefore an assault weapons ban would have essentially no effect in reducing crime, but would certainly inconvenience a huge number of American citizens...who vote!
You can also reference the several research studies of prison inmates imprisoned for crimes using guns.
The largest was a study conducted by two of the most vehement anti-gun spokesmen of their day, Professors James D. Wright and Peter H. Rossi, funded by the U.S. Department of Justice. They performed in-depth interviews with 1,874 inmates who had used weapons in crime, incarcerated in federal prisons in ten states in 1982 and 1983 to determine their attitudes on weapons choice, deterrence, firearms acquisition, and attitudes towards gun control. Wright and Rossi have performed two studies, well worth your research for material to refute anti-gunners! They came up with nothing to support anti-gunners or increased gun restrictions, to their great surprise.
I participated in a similar study in California in 2003...that study was essentially buried as it did not prove the Mayor's beliefs. The 20 inmates that our team interviewed all preferred pistols such as the police carry...small, easy to conceal and use (but not small caliber or cheap pistols). None preferred assault weapons...large, heavy, hard to hide and attention getting, noisy and more complex to operate. (Some owned assault weapons when arrested...but they were for self-protection and recreational shooting, not used in crime.)
There are doubtless other studies...