Hey Goochee, welcome aboard!
Looks like a good start there - are you glueing as well?
For my cocktail I cut the rounded corners with the jigsaw, slow and steady and makes sure your jigsaw is sitting square is about all I could say for the jigsaw. If you have access to a router you could always cut the initial cuts outside the guide lines with the jigsaw then using a flush trim bit and a jig/guide, route to a nice even finish. Even if all 4 corners aren't 100% exact it won't be noticeable to the naked eye. Plus, imperfections can be either routed away or sanded. The T-moulding will help to hide any little boo-boos too.
As for the screen cutout, I plopped the top on the cabinet, marked where the sides were once centred then flipped it, put the monitor face down evenly inside the marks (allowing as well for the thickness of the sides) then mark out where the monitor sits. Then measure how much there is between the outermost edges of the monitor and the panel then adjust the markings to reflect this. This should be the size to fit your panel without showing the surround. Cut it out INSIDE the guides with a jigsaw then tidy up with a router (flush trim bit) being sure to use jigs that are clamped nice and tight. Depending on the thickness of your top you might want to run an angle edge bit around the inside with the router to slope the edges down toward the screen. If you can see any of the monitor surround disguise it with black electrical tape.
If you haven't used a router before be sure to have a few goes on some scrap. Once you get the hang of it you'll love it. They can be picked up for around $50-60 at Bunnings, Ozito is fine for this sort of use - I think Heath has an Ozito? I've got a Ryobi which I'm really happy with.
It's great to see new project on the go here, I can love vicariously through you for the time being until I get my next build organised - probably a low boy unless I get an order for something else!
Look forward to updates mate and ask as many questions as you need to and remember - most mistakes can be fixed/covered up or explained away
Measure twice - cut once!