You may well need to tutor for 11+, at least to the extent of familiarisation with style of exam and learning how to use the time available. So you'll need to research the type of exam your candidate grammars use and decide about whether to tutor and how much (nearer the time).
If you're not close to any particular grammar schools, then DC needs to score a very, very high mark for a super-selective. This can get rather stressy.
Prep schools by and large prepare for exams for independent secondaries, and those exams may be nothing like those for state grammars, so you'll have to check idc if everything which should be covered has been covered, and if it's not decide how you fill any gaps.
That said, if you want to use the independent sector at primary age and maximise the chances of getting the right grounding for an academic destination school, I think you need to look for a selective prep with a good range of leavers' destinations and which does not expect pupils to stay to 13+ (though with the rise of the pre-test, even those schools do year 6 exam prep these days).
(I say good range of leavers' destinations, because if it becomes apparent during the primary years that your DC is not super-selective material, you will still want the school to support all sorts of onward destinations).