I would weld the whole deal, not much point being able to open it up especially on a flat or large finned hot plate... If it had dirty water running through it, maybe, but you should be using basically engine coolant. You really don't want it coming out over the tank.
You also want to force the water to spend some time in the plate, so you really want to channel it. I would make an S type shape, input from one corner, loop back and forth then back out. Along each wall you can add pass-throughs, where appropriate, by substituting part of the wall with a tube, then drilling out the plate.
In the end i would expect something like this:
|------------| V-In
| ----O-----|
|-O------O- |
| ----O-----|
|------------| ^-Out
Size wise i would make the plate fairly thin, channels wide enough that its comfortable to weld. Welding the internal fins to the cover plate will be more 'fun' than welding them to the bottom (where you can weld on the inside). But i expect you know what must be done to weld the fins to the cover.