Solved

Car Development

How should I develop my car throughout the season? Compared to most of the drivers in my league, my development isn't the best and I usually fall off the pace during the middle of the season and catch back up when the other managers can't develop their cars anymore. Also, what is the best way to get good CDs and TDs? I keep looking for them on the transfers tab but no one good shows up anymore. (For context, I am LVL 16)

This answer doesn't quite cover the entire question as getting into complex design strategies definitely deserve their own full answer from someone less tired, but here is a small tip or two:
4.5* CDs and TDs that match your manager level are just as effective as 5* staff. For doctors of course, this doesn't apply.
The most important stats are Acceleration, followed by Handling then Braking and Downforce. Cooling and Reliability are inactive and can be completely discarded. In NRF leagues, FE is also very important. To grossly oversimplify, call it worth developing until its value ≈ 25+ ( [Race length percentage (e.g 25/50/75/100] /2)

No better way of simplifying this than what Rhys posted!