What is the priority order of factors like resonance, hybridization, solvation, etc. in determining the relative acidity or basicity of compounds in a list?

Anything that decreases the #"X-H"# bond strength in the acid or stabilizes the conjugate base will increase the acidity and decrease the basicity of the conjugate base.

I would identify the factors in the order 1. #bb"R"#esonance; 2. #bb"A"#tom; 3. #bb"D"#ipole #bb"I""#nductive effect; 4. #bb"O"#rbitals (#bb"RADIO"#).

Strong acids

There are six common strong acids. In order of increasing acidity, they are:

#"HNO"_3 < "H"_2"SO"_4 < "HCl" < "HBr" < "HI" < "HClO"_4#

Any strong acid is stronger than most organic acids.

Some factors to consider are:

1. Resonance

I put resonance stabilization of the anion first in the list.

The more resonance contributors a conjugate base has, the stronger the acid will be.

That partly explains why sulfuric acid is stronger than nitric acid.

It also explains why acetic acid (#"p"K_"a" ≈5#) is a stronger acid than
ethanol (#"p"K_"a" ≈ 16#).

2. Atom

(a) Acidity of H-X increases from left to right on the Periodic Table.

#color(white)(mmml)"CH"_4 < color(green)("N")"H"_3 < color(red)("H")_2"O" < "H"color(lime)("F")#

#"p"K_"a"color(white)(m)~50color(white)(mmll)38color(white)(mml)15.7color(white)(mm)3.2#

As the electronegativity of #"X"# increases, the bonding electrons are puled closer to #"X"# and the acidity increases.

The exception is #"HF"#, for which the conjugate base #"F"^"-"# is stabilized by solvation by water molecules.

(b) Acidity increases from top to bottom of the Periodic Table.

#color(white)(mmml)"HF" < "HCl" < "HBr" < "HI"#
#"p"K_"a"color(white)(ml)3.8color(white)(mll)"-8.0"color(white)(mm)"-9.0"color(white)(mll)"-10"#

As you go down a group, the bond length becomes longer and weaker, and the charge density on the ion decreases.

3. #bb"D"#ipoles and #bb"I"#nductive Effects

Electronegative atoms draw negative charge toward themselves.

This weakens the H-X bond and stabilizes the conjugate base.

The effect decreases with distance from the acidic #"H"# atom.

(From SlidePlayer)

Alkyl groups are electron-donating groups.

They push electron density onto the #"COOH"# group and destabilize the carboxylate ion.

The more alkyl groups, the weaker the acid.

4. Orbitals

The more #"s"# character in an orbital, the closer the electrons will be to the nucleus.

As we go from #"sp"^3# (alkane) to #"sp"^2# (alkene) to #"sp"# (alkyne) hybridization, the stability of the negative charge increases.

Alkynes are remarkably acidic compared to alkanes.

Here's a summary of the discussion.