In terms of driving aids:
SRF will make you faster in all circumstances, often by a couple of seconds a lap.
ABS on 1 is usually the quickest way around. At least 95% of people I've seen online have it on that setting. ABS on zero can be beneficial to some people, but only really the elite, from what I've seen. It's fun to try, though.
ASM will just kill your cornering speed, and active steering often does the same.
Personally I like the blind spot indicator. Of course it doesn't make you faster, but it does make you more aware of cars around you.
For pure speed, you will want to use the lowest traction control setting you can get away with. Personally I use zero for the majority of cars, and put it on 1 for the most troublesome cars, like the Formula GT.
I use controller sensitivity on 7, but the difference this setting makes is fairly minimal in my experience. It just adjusts how rapidly the wheels will go from lock to lock, so a higher setting is useful for tracks like Monaco. This lock to lock speed is one of two advantages a controller has over a wheel, the other being that your arms won't fatigue in long races on a pad.
Learning to use manual gears will help you improve your times quite dramatically in some cars, and in others not so much. Being able to short shift is great for fuel saving and controlling cars with high power, and choosing your upshift RPM means you can take advantage of a car's power curve. Cars like the Aston Martin DP100 get better acceleration if you shift up early, for example.
In terms of DS3 vs. wheel, it depends hugely on the car/track combination. Cars with limited front grip will generally be faster on a wheel, as the game introduces limits to the steering angle you can use on a controller based on grip and speed in order to make cars drivable. If tuning is permitted, this deficit can be greatly reduced through setup, but if not, there are still a couple of tricks you can employ to help cure the understeer. Firstly, setting your brake bias more rearwards can help the car to bite on corner entry, and secondly putting a harder compound on the rear can help to rotate the car.
GT Academy 2014 was a great example of the advantage a wheel can provide. If I recall correctly at round 2 in the 370z around Apricot Hill, the top controller time was only about half a tenth off the top time and about P5 overall. In the final round at Spa, however, I think there was only one controller user within a second of the top time, as you couldn't take Eau Rouge or Blanchimont flat, or carry the same speed around Pouhon.
I tested the steering lock issue with a few mates at Monza (No chicane) in the TVR Tuscan Speed 6 Touring Car in stock form using RS tyres. Wheel users could take the first corner flat out at ~175mph, whereas controller users had to slow down to the mid 150s or they'd fall off the track. Only being able to carry 85% of the wheel users' speed around a corner will cost you pretty heavily. If only PD could introduce a control whereby we could choose the strength of this steering limiting mechanic, this disadvantage would largely melt away...
If you do decide to get a wheel, it's worth noting that several common ones are not yet supported by the PS4 when deciding which one to get. If you decide to stick with the controller, I'd suggest, assuming you don't already, using L2 and R2 for braking/throttle (or the right stick if you prefer) to give you more detailed inputs than you can with the x and square buttons. Also, the left stick is much better for steering than the directional buttons, I've found.
You can be very smooth on a controller with practise, to the point at which the added smoothness of a wheel would barely improve your lap at all. It's almost all in the turning capability in my opinion!
Anyway, sorry for the lengthy post, and good luck with getting more golds in the future. Practising, be it through racing your ghost or racing players more skilled than yourself, is the key to improving.
