Water – Should I upgrade to 3/4″ pipe all the way to the new pex manifold

I think kitchen sinks are 3/8" (but I can never remember). So you'll want a 3/8" female, 1/4" male, 3/8" male tee. You should be able to find one at the local big box, or hardware store.

Something like this

1. Shut off the water using the shutoff valve.
2. Remove the existing supply line.
3. Attach the tee where the supply line used to be.
4. Connect the sink supply to the 3/8" male outlet on the tee.
5. Connect the refrigerator supply to the 1/4" outlet on the tee.

NOTE: Use your preferred pipe dope method (tape or goop), however, since it's a brass fitting dope should not be required.

That looks perfectly suitable. One additional thing you should be aware of, though - if your existing plumbing contains any yellow brass fittings, they really need to come out because of a chemical quirk of PEX; the zinc gets leached out of yellow brass, leaving behind only soft copper, and the fittings may either leak or plug solid. You can use RED brass, just not YELLOW brass.

The manifold should be one size larger than the pipe supplying it.

If there's any question at all about grounding, a solid ground rod can be driven... with the result of giving you a better ground than you ever had by grounding through copper pipe.

Like copper, PEX requires a 1/4" drop per foot (never install it level or wavy), and requires a drain at every low point so the house can be winterized if necessary.

Is there any particular reason for going with PEX instead of tending to leaky fittings as you find them? I suspect that those fittings were always leaky because they were never sweated together correctly in the first place. I ask this question because replumbing the entire house in PEX is really a large, expensive job... while replacing (or resweating) one fitting at a time is relatively cheap.