I am so fed up with getting wet. Could someone please recommend a coat that starts out and remains waterproof and boots that don’t let in water.

If you mean wellies, Ive had my Le Chameau for about 10 years and they're still going strong.  Expensive though.  They are knee high and I chose to buy the neoprene lined ones for extra warmth although I actually now find I don't need the extra warmth in the leg.

Ditto here with Le Chateau. Mine now 20 years +. And still sturdy and in good order save the calf adjustment things which are broken but not necessary anyway.
Aigle also good make.
Re- waterproof go for long length. Waxed jackets get sodden but keep you dry but take a long while to dry out .
Outdoor and Country online is a great resource.

Whoops!
Le Chameau
Not Le Chateau
Vive la difference!
I should know.
Predictive text to blame.

It's a camel .I know of  the make.but never looked it up before . Yep totally different to a chateau lol
You can see french isn't my forte !

But Italian sure is !
Viva forte!

I hope you took that as the compliment I intended.

Of course lol

Either Le Chameau or Aigle.. ive got Aigles. 1st pair lasted over 10yrs. New pair over a few years. They are the same as Le Chameau, just slightly different fit on the foot, which works better for me but they are pretty much the same