There is no hard and fast rule to answer this question, what works best for one person may not work at all for another.
When analyzing the possible arts available I believe the answer is dependent upon the practitioner and the fighting range.
What works for one person’s body type may not work for another, personally I don’t bend / flex well, so learning Tae Kwon Do doesn’t suit my body type, but Kung Fu is more suited to me.
Best striking art to combine Judo+BJJ
To say that one martial art is ‘the best’ to work with BJJ / Judo is a fallacy, it has to be ‘what is the best martial art’ for ‘me’ to work with BJJ / Judo.
When looking at the options, fighting range is my key criteria. What is my optimal distance for striking an opponent, am I better at kicking, punching or am I an elbows and kneed type fighter ?
When you have experienced multiple arts for a long enough period you can get a feel of the effective fighting range, that is when you can work out if it blends well with the BJJ / Judo combination.
One other consideration that isn’t in the perfect world scenario is availability. If someone tells you that art X is perfect but the only instructor is 500 miles away, how long will you maintain those classes ?
If you live in a metropolis then the availability of classes may be a moot point, but how much effort are you prepared to put into traveling to a class.
I would suggest spending a minimum of six months taking classes in a variety of striking arts that are local to you, then select the ones that fit in with your training schedule the best, it may be only one or it may be that you find several classes that suit your fighting style.
I recommend that you also mix the nationalities of the styles, don’t just focus on Chinese of Japanese arts, there is a world of styles out there, mix and match.
Remember that in a fight, be it a ring or a street fight, it is almost impossible to defend against an attack that you don’t know exists ! So if you find an esoteric striking art that nobody has ever heard of you will have an immediate advantage !