I have a T3 in 7mm for hunting out west and here are my suggestions:
Rings - Hawkins Tikka direct mount, https://bertrambrass.com/product-category/hawkins-tikka-rings/
Optic - Find a Bushnell LRHS in the classifieds or if you want to up the budget, Leupold Mark 5HD 3.6-18x44.
Other mods -...