Honestly, at primary I don't think it matters that much. A few clubs in whatever your children find fun and interesting will be plenty and you will probably find that the schools offer quite a lot of clubs and activities, usually after school.
DD went to state primary and is now at a good private secondary in her GCSE year and at primary in different years she did choir, musical ensembles (she had recorder, ukulele and guitar in different years as part of the curriculum and did violin and piano in school time as part of the county music services), yoga, sewing, musical theatre, tap dancing, French, ballroom dancing, maths (fun logic puzzles rather than curriculum), extra ukulele, athletics (as part of county schools competition) and probably more things that I have forgotten! There were a ton of others - gymnastics, ballet, football, police cadets, coding, animation, art, chess, I can't even remember them all! I don't think her school was unusual. It was a very ordinary primary and although it was in a nice part of London it had a very mixed catchment.
Most of the clubs she did at school were either free or very low cost.
Out of school, the only things she really did were ballet and drama and she has continued with the drama club but only did ballet when she was quite small.
One thing I would suggest is swimming. They did not get a lot of this at state schools and it's an important skill. DD didn't do much (I think one six week summer holiday course) because she really hated it but I think if I did it all again I'd make more of an effort to keep her going longer.
I don't think you need extra maths or English tuition unless you feel your children aren't keeping up or need extra help or maybe some to help with 11+ prep later on.
If you decide later on that a private secondary would suit your children better, it is absolutely possible to get in from a state primary. The thing that helped us most here was some exam technique preparation which you can get from a tutor or do yourself. Some people also tutor at this point to teach extra content which may also be helpful.