My level of involvement with computational chemistry would also be best described as dabbling, but here goes...
Anything having something to do with "force fields" relates to molecular mechanics or dynamics. Force fields are instructions
on how to account for the interactions involved in making atoms stick together (bond lengths, e-e repulsion, etc..)
Since force fields are at least partially experimental, some force fields are better parametrized for different applications.
(CHARMM & AMBER for biomolecules, for example.)
I don't know the specifics of what goes on with the force fields provided as defaults with Avogadro, and their wiki isn't
too helpful on the subject, just stating that,
MMFF94(s): organic chemistry and drug-like molecules.
UFF: This force field can be used across the entire periodic table.
Ghemical: simple organic molecules
As you probably have noticed, even though UFF is said to be parametrized for the entire periodic table, that's bit
of a stretch.
For the next question, let's divide the abbreviations into two groups: (1) AM1, MNDO, MNDO-d, PM3, RHF, RM1, MP2 and (2) B3LYP
The first group is wave-function based "Hartree-Fock" methods. Most of them either contain more elaborate ideas than "just" RHF, or
are semi-empirical. How to choose which method to use depends on what question you are trying to answer, and the size of your
molecular system. I'd recommend googling around for more detailed descriptions about each one.
The second group is for the sole representative of density functional theory. DFT differs fundamentally from HF methods. The B3LYP
functional is probably one of the more commonly used for modeling small organic molecules. The appeal of DFT is that it tends to be less
computationally demanding than comparably accurate HF-methods.
The "Basis" dropdown refers to the basis set to be used in the (either HF or DFT) calculation. In addition to the level of theory, the chosen
basis set has a huge impact on both the accuracy and time consumption of the calculation. I'd suggest referring to a book on computational
chemistry for specifics on the basis sets. In short: bigger is better, but makes for lots of more calculations.
"Calculation" dropdown lets you choose what question you are asking about the system. For a new structure, the first thing you probably
want to do, is optimize the structure at some level of theory, and then go on about calculating the frequencies, or some other properties.
You can also mix & match, by optimizing the geometry with molecular mechanics and doing the frequency calculation using DFT or HF
methods.
The abbreviations are unfortunately cryptic (I have no idea what some of them mean), but at the same time they contain a lot of
detailed information to the specialist.
Sorry for the roundabout response, books are written about these things for a good reason
Basically, if you are just playing around on your desktop, you probably want keep mostly on the molecular mechanics side of things
since it's the least demanding method of the three. Both HF and DFT start getting quite heavy really fast (from a desktop perspective).