A quantity is dimensional if you can rescale it and all the relations remain the same. It is dimensionless if the numeric value has direct meaning in the equations.
Distance is dimensional. Whether you use meters, feet or astronomical units, the relations with them stay the same, except related units, e.g. velocity, scale along with it. But angle is dimensionless. The value in radians is a ratio of lengths and if you use degrees instead, a conversion factor pops up in the relations. And bit is also dimensionless, being the 1 of information entropy, defined in terms of counts and probabilities.
Now the dimensional quantities are still related to each other. 432
Since velocity is distance per time, if you scale the distance unit, the velocity unit scales with it.
The base units are a set that can be scaled independently of each other (in your problem domain!). Note that the choice is somewhat arbitrary. For example electric current was selected as base dimension, but electric charge would arguably make more sense. The other units are derived.
The problem domain is actually important. It turns out plenty of constants are actually just conversion factors due to choice of scaling. For example once special relativity gets involved, time becomes just another spatial dimension, distances can be measured in seconds, and velocity becomes a dimensionless ratio.
In fact, all the dimensional constants ones are and the natural units, especially in the planck variant, leave you with no dimensions at all and only the three dimensionless constants $\pi$, $\alpha$ and $\alpha_G$.
On the other hand, there are cases where you can distinguish, say, parallel distance and perpendicular distance and then suddenly angle becomes perpendicular distance over parallel distance and is dimensional. If in what you do you don't mix the two, making them distinct units significantly improves utility of dimensional analysis as a verification.
The SI base units were simply chosen to be practical for classical physics and everyday engineering and is somewhat arbitrary (especially the candella, unit of luminous intensity, is not really a basic unit; it is just energy weighted-averaged over light spectrum using specific weighing function). 432