All trains are divided into several classes which unify their usage and stats. In general the main purpose of a train class is to mark trains which work similarly and are just improving over time within the class as new models get introduced.
You can find the train class in the purchase menu info in the bottom, and also the coloured numbers indicate the class and id in that class.

Note: train speeds are in the code values. The in-game values might be a few km/h higher, but they count the curve length speed from the code values so those are the important ones to mention.

Superstrong class

While being the slowest class of all, the magic of those trains is that they are extremely powerful so you should never need two engines per train, and there are two sub-classes where one allows CL1.5 and the other CL1. Superstrong trains are 1 tile long so once you replace to them, you cannot automatically replace back to any other class (except slugs). This makes them effective if you use long trains with short curves, hills and so on.
Meet the Monster goes 105 km/h with CL 1
X E Qt R goes 133 km/h with CL 1.5

Strong class

The strong class benefits from very high power and tractive effort, while being slower than most classes. Anytime you want lower engine count, thus increased capacity of your trains while keeping great acceleration, Strong class is the way to choose.
Duke NUT’em goes 160 km/h with CL 3

Medium class

Rail medium class

In general the average engines provide good stats all around. When using just a single engine for short trains, their acceleration is not amazing, but acceptable – while keeping the high capacity. If you however use more engines, you gain Strong-like acceleration for the cost of capacity - while keeping Medium speed.
Mastermind goes 197 km/h with CL 4

Monorail medium class

The reduction of tractive effort per added unit means that these trains are especially effective when used with short trains, but they are still acceptable for average trains. Tractive effort is a very important value which changes mainly acceleration at low speeds, but does not differentiate the total acceleration trail lengh as much. Longer trains can benefit from +50% curve speed for monorail, compared to normal rail.
I Choose Noise goes 300 km/h with CL 3

Maglev medium class

The most important aspect of maglev tracks in general is +100% curve speed in compare to rail. To this adds the fact that maglev cargo wagons are short which lets them travel through curves even faster. Maglev medium class is extremely effective if your network gets messy as it deals with short curves very easily. The full speed still is CL3 but shorter curves do not hurt much. All this is for the cost of very low capacity however.
Get Heavy goes 400 km/h with CL 3

Fast class

Rail fast class

The train class which is based on very high speed lacks a lot of acceleration. However, because of the heavy rail wagons with high capacity, it has very high throughput capabilities if you boost their acceleration by some aid to their acceleration - like making them accelerate on a downhill.
Banshee goes 255 km/h with TL long curves

Monorail fast class

As this class grows with power every time a unit is added to the train, the fast monorail class reaches it’s maximum effectiveness when used with very long trains. The power grows until 20 units are in the train so their effectiveness is maximal with 10 tile long trains. Their high speed however means that you have to keep as long curves as your trains which can get very space consuming. The Maximum pain has maximum curves capped at CL6.
The Reality goes 415km/h with TL long curves

Maglev fast class

The fastest of all cargo trains are truly fast, but their effectivity is mediocre in general. Unless you use any mechanisms which would help with their acceleration, you cannot do much to help them as downhill acceleration does not apply nearly as greatly as for rail fast trains.
Speed Demon goes 500km/h with TL long curves

Chameleon class

Flexible stats: An unique class of weird trains which change their maximum speed according to their length – shorter = faster. As their power stays, they get a bit better acceleration with being longer. They can travel through very short curves because in short form they do not even mind them and when longer then they travel slow enough to pass through the curves without slowing down.

Wagons: These trains have rather low cargo capacity in wagons and relatively long loading time of 7 stages

Engine cargo capacity: Their power is considerably high, especially because their engines have 50% wagon cargo capacity - meaning you can use multiple engines with not much penalty to capacity.

14 cargo units per engine also means that these trains are extremely effective when used with short trains (especially 1-2 tile trains) as there the engine makes 25-50% of the whole train.
They are also the only engine which can be used in train length 0.5

Usage: Chameleons are generally a very comfortable and all-around good engine to use. In short forms they are fast and effective, in longer forms they shine in utility of short curve requirements, making them good precedessors for future slug networks.

All of their vehicles consist of 2 articulated parts, making them travel through curves faster, but they cannot be flipped by ctrl+click in depots. To make this look nice, they automatically flip when at the rear of the train. When the engine is in the middle of the train, middle unit shows as one of the wagons, attempting to be closer to one of the train ends (depends where it is put).

Note: Chameleon trains change colour randomly upon station/depot visiting.

Destroyer of Worlds goes 323km/h base speed at 4 units (engine and 1 wagon), decreasing by 7km/h with every added unit. The cap is at 28 units with 148km/h. 2 units (engine only) get a speed bonus to 355km-h which is especially considerable if you want CL1.

The MEOW class

Special trains which change their stats based on which railtype they travel on.
This means they are extremely flexible as you can use your desired configuration the best way you see fit.
In general their raw stats are rather low to make them weaker over all. But if you can use the bonuses to your advantage, then they are very effective.

Rail MEOW

With PURR railtype does not matter much, but rail means rail wagons which gives the benefit of 3rd gen wagons.
All rail MEOW trains are 1-tile long articulated steamers, which means if you use only one the engine part is always going to be at the front of the vehicle,
therefore the stats change as soon as front head of train reaches the next colour.

Transgenic goes 170km/h without bonuses - CL4

Monorail MEOW

Monorail wagons are a bit smaller than rail, but the train speed compensates that.
The main difference is that all monorail MEOW trains are dual-headed, which means the engine is always at both ends of the train.
That way the stats change at different times, which can be used in various other ways.
If each train head is at different colour, each of them gets it's bonuses appropriately - for example half bonus for power and half bonus for tractive effort.

Spectrum of Eternity goes 250 km/h without bonuses - CL3

Mentally Disturbed class

In case you feel your trains are way too normal, you can always switch to the trains with the power of the rainbow. Not only are these trains slightly abnormal, but they also are living beings with feelings and stuff! Any depot or station visit will cause these trains to change mood, which also changes their face - and power. These trains have considerably lower throughput capacities than other "normal" classes however.
Brainmelter goes 236km/h in CL3

The SLUG class

Utility and fun class which is extremely effective in networks where you cannot afford longer curves. Their raw throughput is quite low due to slower speeds than medium maglevs, even though their wagon capacities have 2 more units per wagons. While the Animal Express comes a lot earlier in the game (2016), it is slower.

Animal Express has therefore lower total throughput capability, but it can actually be viable to autoreplace back to Animal Express in the very very very late stages of the game, when their CL1 is helpful, even though Slug does not slow down in CL1 too terribly much either.

Rainbow SLUG is just a visual upgrade of the normal SLUGs, causing them to be much more awesome.

Animal Express goes 211km/h in CL1
The SLUG goes 265km/h in CL1.5
RAINBOW SLUG goes 265km/h in CL1.5

WETRail vehicles

Apart from their visual appearance, ships can be very a powerful tool.
The class of small ships is very effective with refit networks due to their friendliness with depots (low speed) or high throughput in stations (high capacity).
The special small ships - animal ships - are noteworthy due to their increase potential when loaded - by eating cargo and gaining additional power. Bonus small ships also fake their max speed to gain higher ratings at stations - and more cargo.
Large ships are great in raw capacity, but their loading speed is very bad (9 loading stages).

SMALL SHIP goes 88km/h in CL1
LARGE SHIP goes 88km/h in CL1