As others have said, there is no protocol, just what you're comfortable with.
I do road rides and occasionally mountain bike rides, no cycling for transportation. When I first started I wore cotton t-shirts. Cotton is not the most comfortable fabric, and the t-shirts tended to be too loose so they would flutter or balloon up as I rode. Bike jerseys tend to be more fitted and more breathable, therefore more comfortable. And the pockets are useful.
I like to shop and I get bored wearing the same thing over and over. And I like to wear the best possible outfit for the weather. So I have lots of jerseys. Long sleeved thermal, long sleeved regular weight, short sleeved regular weight, short sleeved lightweight, sleeveless, tank tops with built-in bra. Arm warmers (thermal and lightweight), arm coolers for warm weather, DeSoto Cool Wings (wicking bolero jacket) to wear over tank tops to protect my shoulders from the sun. Wind vests, wind breaker, water-proof and windproof jacket, wind resistant thermal jacket. Long sleeved wool base layers to wear under a jersey in cooler temps.
I prefer bright colors, avoid black (too hot) and most shades of blue and green (not visible enough from a distance). I like reflective materials on the jersey for when I ride after dark or on cloudy days. I don't like elastic around the arm openings or the bottom hem.
The brand is not important to me as long as the fit and fabric are good.
- Gray 2010 carbon WSD road bike, Rivet Independence saddle
- Red hardtail 26" aluminum mountain bike, Bontrager Evoke WSD saddle
- Royal blue 2018 aluminum gravel bike, Rivet Pearl saddle
Gone but not forgotten:
- Silver 2003 aluminum road bike
- Two awesome worn out Juliana saddles