I ask mainly because I am not familiar enough with newtonian mechanics and higher-level physics in general to know the repercussions of such a change, but on the simpler plane of existence, I have been given to understand that data is lost about an object's motion when you go from velocity to acceleration, due to something I will learn when I formally take Calculus (of which I have a fairly limited knowledge). For instance, in a velocity vs. time graph, one can observe the object's acceleration (a term which I would redefine in my system), its velocity, and its direction, as well as jerk and so on. Taking the first derivative gives the current definition of acceleration, which only shows acceleration (as it is currently defined, the rate of change of velocity) and jerk, etc. However, the sign of the acceleration is of nearly no consequence. In my system, the sign of the acceleration would indicate acceleration (in my terms, the rate of increase of velocity) or deceleration (a term not commonly used by physicists). Basically, I would like for acceleration to mean more than it does currently, and I am wondering if this would negatively affect high-level derivations of simple physics to the degree that it is simply incorrect.
Conventions are typically used because the larger body of people found them to be the most effective way to express things. Acceleration is the first derivative of velocity because people have found that that's the most useful value to capture and give a name!
The big issue with your approach appears when you consider systems that are more than 1 dimensional. Accelerations and velocities are not always in the same direction. They may be at right angles, or at 45 degree angles, or any other direction.
This shows up quickly when you try to adapt F=ma to your system. This means that the force must also be in the direction of motion, but it should be very clear that forces are not always in the direction of motion.
More issues will crop up as you learn more calculus based physics. The equations of motion are quite simple when defined in the way people generally define them. Your system would add many extra layers of complication to those equations. You'll have to take my word for it, until you learn more calculus based physics, but hopefully the directional issue will be enough to convince you to use the definitions everyone else uses.