Sulfasalazine isn't nearly as hard on the kidney and liver as most other DMARDs. It can cause stomach ulcers though.
When I started SSZ, it did initially raise my liver stats, but those went down in about a month or so. What really hit my liver was the Methotrexate.

Either way, your doc should keep an eye on those values just in case.

Wishing you the best of luck!