Is it considered proper English to say "You best be..." or "You'd best..."?

"Had best" is correct, but "had better" is more common. "Has best" is usually associated with dialects, such as in the American South. Source

One can think of them as forms of:

It would be better if you did that.

It would be best if you did that.

"You best" is slang, omitting the 'had', and not correct.

Sentences such as You'd best be going and You'd better be going are fairly common in British English and You best . . . might occur as an elided form of You'd best . . . They are perhaps most frequently found in speech, but I wouldn't be surprised to find even in some academic writing something like I had better set out my position now to avoid misunderstanding later on.

"Forgotten" or "forgot" as past participle of "forget"

Meaning and origin of "That dog don't hunt"

Is there such an $x$ that both $2^{\frac{x}{3}}$ and $3^{\frac{x}{2}}$ are simultaneously rational?

Prove or disprove that in an 8-element subsets of $\{1,2…,30\}$ there must exist two $4$-element subsets that sum to the same number.

On the formula, $\pi = \frac 5\varphi\cdot\frac 2{\sqrt{2+\sqrt{2+\varphi}}}\cdot\frac 2{\sqrt{2+\sqrt{2+\sqrt{2+\varphi}}}}\cdots$

Proof of a new identity for the finite sum $\sum _{k=0}^{n-1} (-1)^k \sec \left(\frac{\pi\, k}{n}+\frac{\pi }{2 \ n}\right)$

Basic counterexample re: preimages of ideals

Homogeneous topological spaces

Liouville's theorem for Banach spaces without the Hahn-Banach theorem?

If $G$ is biconnected and $\delta(G) \geq 3 \Rightarrow \exists v: G-v$ is also biconnected.

A generalized (MacLaurin's) average for functions

Twisted Cech cohomology