I want to convey the feeling that "do whatever you feel is the best"? How should I incorporate the phrase "deems fit" in my sentence?
As Mick mentions in his comment, "to deem fit" is a little old-fashioned but not, I think, enough that you shouldn't learn how to use the idiom. I wouldn't call it "Victorian" English, as it's a phrase that sees regular use even today.
This answer by Tom B is the best rephrase of your sentence.
Do whatever you deem fit
Pick whichever person you deem fit for the job.
My path is mine to walk as I deem fit.
This plan of creating an electoral college to select the president was expected to secure the choice by the best citizens of each state, in a tranquil and deliberate way, of the man whom they in their unfettered discretion should deem fittest to be the chief magistrate of the Union.
"Deem" is itself a verb meaning "to judge" or "to consider (in a specified way)". You can, conceivably, deem anything but it's a word that is more commonly associated with words like "necessary" or "proper", or used alone:
It's clever enough, but the question is whether future generations will deem it "art".
Jackson spoke, relating all he deemed pertinent.
I am trying to make a point about the fuzzy edges of what has been deemed a "disease".