Best Mechanical Gaming
Best Wireless Gaming
Keyboard→Logitech Wireless Illuminated Keyboard K800($100)
Best Gaming Keyboard Overall→Logitech G710 Plus($130)http://www.tomsguide.com/us/best-gaming-keyboards,review-2009.html
Best All-Purpose Gaming
Mouse→ Logitech G502 Proteus Core($79.99)
Best FPS Mouse→Corsair Vengeance M65($57)http://www.tomsguide.com/us/best-gaming-mice,news-18236.html#xtor=EPR-8886
Choose whichever combo fits in your budget.
Edit: For $100 budget you can get along with Razer BlackWidow and Vengeance M65 which will make total of $110. It will be $10 more than your budget but totally worth it.