Being specialist for gums, I will advise you to go for scaling but scaling will remove only the yellow stains which are present on your teeth. For your gums, I mean for blackish pigmentation which is present over your gums ..it is because of melanin hyperpigmentation, its physiological so no need to worry, you just go for the treatment as gingival pigmentation in which they remove blackish part of your gums and after healing they will appear as pink only. Nowadays gingival pigmentation can be done using laser also which is painless.
Next Steps
you should get scaling of your teeth done. Simultaneously you can go for the treatment of Gingival Depigmentation, For the treatment of your black gums