[Chris is me]

The "standard" drive, IMO, is #35 chain and sprocket off a gearbox for each side of the drivetrain. I think it's best to analyze things relative to this, as it is a very solid standard and also happens to be what the kit bot is based off of. It's also probably the simplest.

The most common deviation from that is direct driving one of the wheels. If you do not have a sprocket reduction or can incorporate that sprocket reduction into your gearbox, you can feed the output of the gearbox directly to a wheel on your drivetrain. This saves the weight of a sprocket / chain run and ensures in the HIGHLY unlikely event of multiple chain failure, you will still be able to move. Generally, this is done in 6 wheel drive setups, direct driving the center wheel. This allows you to bolt 2 sprockets to that driven wheel, chain those to each of the outer wheels, and call it a day.

From there, you can get more creative. A wheel driven by a moving axle is the first part of a live axle drivetrain. While dead axles have the advantage of serving double duty as standoffs that work to structurally reinforce your chassis, occasionally you may see value in using a live axle as it allows you to put your wheel sprocket anywhere on the driveshaft, not necessarily next to the wheel. The most common use of live axles is in cantilevered "west coast" drivetrains; these somewhat complex (relative to the kitbot) drivetrains run the wheels on the outside of the chassis member and the sprockets on the inside, necessitating a live axle.

Moving away from #35 chain is not something to take lightly, as chain is (relatively) easy to work with and allows for some error in design. Moving to timing belt and pulley instead of sprocket and chain is certainly doable, but it requires a lot more planning in advance as you have to order and design around an exact, non-changing belt length (as opposed to roller chain which you can adjust). Gear drives are even more sensitive as idler gears need to be placed in precise points along the drivetrain; they also take a lot of work to reduce weight to an acceptable level. In general, I wouldn't recommend a team pursue either option without pre season prototype experience.

I'll leave discussion about 4wd, 6wd, mecanum, swerve, etc. out of this post because it's not what you asked about, but I do want to leave a note: When in doubt, 6wd.