Hi David. Ken from Maple Ridge here. I'm a concrete contractor and here is
my 2 cents. You have asked how high, wide and deep, right?

#1 Height
Here's something to ponder: Is there going to be grass next to the new
fence? I'm asking because you could actually set the elevation of the
concrete curb to your desired lawn height. Then mowing is much easier.
(you'll be able to drive or push your mower on the curb.)
Personally, if you don't mind weedwacking, it will be more visually pleasing
if you do pour the
curb slightly higher than the lawn or any other landscaping.

#2 Width
Since you DO know how to weld, why not make up some small steel plates with
anchors on the bottom and actually pour them into the new concrete at the
required spacing? After the forms are stripped, you'll be able to weld your
fence posts to these. Not very nice if you ever have to remove a section,
but it may work better if you will never have to remove them. With the
plates installed in the curb, you'll be able to go with a 8 or maybe even 6"
width.

#3 Depth

DO NOT get a curbing company to do this for you. They do not pour the
curbing deep enough for adequete frost protection and you'll probably be
able to just push over the fence after you mount it on the curbing. IF you
want a permanent fixture, I highly recommend a small (but necessary) footing
under your curb. You can easily get away with 16" wide and 4-6" thick. Pour
the curb on top of this to whatever finished height you decide on.

#4 One More Thing
A couple rows of 10mm steel in the footing and a couple more in the curb
will reduce movement in the curb after it cracks. IT WILL CRACK! You didn't
mention the length of the fence, but it will have to crack to release stress
due to freeze/thaw and shrinkage.