Fundamental questions in a choice of antenna design are:

Does it have the proper polarization (vertical, horizontal, or circular)?

Does it have the proper radiation pattern?

Some secondary issues are:

Will the antenna be small enough for the space available, at the desired frequency?

How will it be mechanically supported, without interfering with the electrical properties?

Will nearby objects interfere with it, or assist it (e.g. car roof as ground plane)?

What type of matching network will it require?

The mode does not matter at all. The frequency only matters as it affects the size and therefore what is feasible.

You've said you want to do 2 meter FM, and that means that you will want vertical polarization. (This mainly means you don't want to build a horizontal dipole, which is a shame because it's really simple. Vertical dipoles work fine, but you need a horizontal structure to keep the feed line running away perpendicularly, which is why it's rarely done.)

This leaves you with a wide variety of vertical antenna designs — ground plane (with radials, or mounted on a metal roof), J-pole, bazooka dipole, coaxial collinear, et cetera. These can all work; it's largely a matter of what you want to build.

However, one factor we haven't yet addressed is the radiation pattern. You said “non-directional”, but there's no such thing as a truly omnidirectional (isotropic) antenna. Any so-called omnidirectional vertical antenna will in fact have a null pointing directly upward. In between directly up and horizontal, the pattern depends on the antenna design, as well as how high above the earth it is. What you want depends on the environment you're in and how stably actually-vertical your antenna is: if you have it mounted in a fixed location with an unobstructed horizontal view then you can benefit from using a higher-gain antenna (more horizontal, less vertical pattern).

Overall: Don't worry about it too much. Given that you're building your antenna, it's likely much more important to pick a design that you can build accurately and tune easily (because small variations in length can matter a lot for VHF).