Your question is a bit tricky, because "most common" is a very vague statement. So I'll interpret "most common" as "textbook". Opening Binney & Tremaine's Galactic Dynamics (2ed) text, which is as far as I know the standard text for the dynamics of stellar systems, the models described in the relevant section 4.3 are Plummer, isothermal sphere, King, double power laws and Michie. Double power laws, as far as I know, are not usually used for GCs. The Plummer is occasionally used, but only for the extreme simplicity of the potential (with finite mass) and so only as a toy model. That leaves the other three.
The isothermal sphere is mentioned as simple, but with the pesky feature you mention of having infinite total mass. The King model is an adjustment of the isothermal sphere at large radii to make the mass finite. The Michie model is a further refinement of the King model to allow for velocity anisotropy. All of these are "commonly" used to model GCs.
Later on, in section 7.5, it is mentioned:
A DF [distribution function] that satisfies all of these criteria is
the Michie DF of equation (4.117). Thus, the Michie DF provices a good
empirical model for the DFs of globular clusters and other relaxed
stellar systems.
The criteria mentioned are, paraphrased: (i) approximately isothermal in the middle, (ii) isothermal density profile in the relaxed region, (iii) few stars with angular momenta exceeding some cutoff motivated by the limit for bound orbits, (iv) DF goes to zero at the escape energy, (v) extended region where the number density goes to zero at large radii, (vi) isotropic velocity in the middle, bias to radial velocities further out.
For what it's worth, this essentially agrees with my (by no means extensive) experience with GCs in coursework, the literature, and various talks.
