As for the bonuses, well they work on a different system, size does not play a part in the bonuses, as the bonuses are determined by ship type and then class.
As you likely already know there are 4 class types, C, B, A and S, C being the worst and S being the best.
For this, we'll just go over the S class bonus range but all classes can be found in the handy table below.
Shuttles at S class have their Damage, Shielding and Hyperdrive somewhere between 15 and 20%, they are all done individually, so they won't all be the same as each other, well, they can be, but it is rather unlikely.
They have a medium level of maneuverability and a base launch cost of 16.67%.
If you really want that Shuttle model you just saw, the S Class could be of some use, and bonuses aren't everything, but they are substantial on the correct ship.
Explorers, as I said before, heavily favour Hyperdrive bonuses with a standard buff to shielding, the S class explorers will have somewhere between 50 and 65% for their Hyperdrive bonus and 20-25% for their shield bonus with no Damage bonus what so ever.
Their maneuverability is very high and they have a very low base launch cost of 12.5%.
Fighters weigh heavily toward Damage, so an S Class fighter will have a damage bonus of between 55 and 60%, a Shield bonus of between 15 and 25% and 0 for its Hyperdrive bonus.
A fighters Maneuverability is also very high matching the explorer yet has a base launch cost of 25%.
Haulers weigh heaviest in the Shielding to protect its goods, so have a Shield bonus at S Class of between 55 and 60%, a Hyperdrive bonus of between 30 and 35% and 10-20% for Damage.
Haulers have the lowest maneuverability of all and a high base launch cost that matches fighters at 25%.
The last being the Exotic is an interesting one, that can only be found as an S Class, and if you remember from the previous slot talk, can only be found in one size.
So an exotics bonuses will always be within this range, which is a Damage Bonus of between 35 and 50%, a Shield bonus of between 55 and 60% and a Hyperdrive bonus of between 50 and 65%.
As you can see, the Exotics low slot count is a trade-off for its very high bonuses and they make a very good general exploration ship.
The last thing regarding these basic stats and such that you should know when looking for ships is the price and what you should expect to have ready for any particular ship you are looking for.
It's a horrible feeling to have saved up your units and waited hours for the perfect S Class Hauler to realise you are 20 Million units short.
To plan ahead and know what you're dealing with, let's go over the system.