The longer you cruise message boards the more of these threads you see. Brake fluid selection is forever a topic of debate. The final decision is always yours.
I have my preference and my choice may not be right for you. Nonetheless, I'll give you my succinct take on pros & cons. Only you can make the final choice.
DOT-5
Racers hate DOT-5. Their reasons range from difficulty bleeding to poor pedal feel.
Weekend drivers with restored cars love DOT-5 because it lasts longer than anything else and won't attack paint. Its ability to collect and pool water in the system is documented, but most collector cars are so frequently maintained that this is not an issue.
Daily drivers don't often use DOT-5 because it is expensive and more difficult to find (as mentioned above).
DOT-3
IF your car has all new brake rubber (not old and not NOS) then you probably can run readily available DOT-3. It's fine. The only caveats are you need to flush and bleed the system every couple of years and you need to keep it off the paint.
DOT-4 (Castrol LMA)
This was probably used in your car when new. When you can find it, it's great. The same caveats apply as for DOT-3... regular maintenance and keep it off the paint. It is (was) also harder to find.
DOT-5.1
This appears to be the current favorite among my acquaintances who race. I have no experience with it. However, do not confuse it with DOT-5. They aren't similar chemically.
What's right for you is largely a function of how you plan to use your car. In my case, both my LBCs are weekend restorations. I run DOT-5. I did not have the difficulty bleeding the system that others complain about. I don't think my cars' brake pedals feel bad either. I did experience the hydraulic brake switch failure that was mentioned above.
The strongest warning I will give you about your selection regards the age of your car's brake rubber. If your car was made before the mid-1970s, you REALLY need to be 100% certain that the rubber in the car has been replaced with the later compound before you consider running DOT-3. DOT-3 will attack the "natural rubber" used in the brake seals of early cars. However, this is not limited to the caliper/cylinder seals. The fluid can also attack brake hoses, proportioning valves, and brake servos. You need all the rubber to be new (later formulation) before you consider DOT-3.