Use a router with a plunge base and either an edge guide or straight edge, depending on the size of your work piece. Attach stop blocks to the workpiece and/or straight edge (clamps would be one easy way to hold the stop blocks in place). The stop blocks will prevent you from cutting your slot too long. First set up the edge guide or straight edge with the appropriate offset for your router base, parallel to where you want the slot. With the router unplugged and the bit almost touching the wood, position the router bit where you want the slot to start. Then use the router base to gauge exactly where to position the stop and clamp it in place. Do the same for the other end of the slot, then proceed with plugging in the router and cutting the slot in several passes, going slightly deeper each time.
You can also use a router table to do something similar, but the steps for setup will be different since you won't be able to see the cut as you're making it. However, you will be able to use your router table's fence and possibly other T-track or miter track accessories.
Although your material isn't very thick, it's still not a bad idea to cut the groove in multiple passes.
In a pinch, you can also use a Dremel/rotary tool (which is essentially just a tiny, low-torque router) along with a router attachment and multipurpose spiral bit, but a router will give you slightly better results.
If you don't have a router, it's relatively easy to cut this slot by drilling a series of overlapping holes with a drill press and Forstner or brad-point bits, then clean it up with chisels.
No matter what solution you use, be sure to put a sacrificial piece of scrap wood on the back side of the workpiece to help prevent blowout when you cut all the way through to the other side.
It sounds like you have a very sensible and thorough approach to the project. Just a few suggestions:
Saw Blade
Most blades that come with table and miter saws are fairly low end. If you are cutting plywood for finish carpentry, you want a high tooth count blade for smooth cuts. Check out one of the blade manufacturers for the range and you will find some recommended for this type of work. The cost is worth it and it will last through many more projects.
Angle cuts
This is where your cut-twice idea is a good idea. You are just trying to replicate a given angle. Measure the angles either with a protractor, or, if the piece being matched is an angle cut across a short dimension (rather than a long bevel) lay it up against the angled saw blade to check.
Use scrap wood to make a try cut angle based on your best estimate. If it is off, adjust the blade or angle guide slightly and try again. When you have the exact angle, cut the good wood.
If you need to make an angle cut on a wide board on the table saw, consider an adjustable taper guide that runs along the fence.
Materials
It wasn't clear to me whether you were going to make the face frames out of pine or just make mock ups and then use oak. For the actual frames, use oak. It is both more rigid and much less prone to seasonal change. All woods shrink and swell somewhat, even when well sealed, but softwoods much more so. You could find shifting of doors and binding drawers if you use a wood that changes much.
Cutting on/next to marking lines
It doesn't matter. What does matter is consistency. You need to know where your mark is in relation to the exact measurement, and cut accordingly. And do the same thing every time.
For example, if you measure a board using a rigid rule, and you mark with a pencil, you can have the far edge of the pencil line at the exact distance. The thickness of the line is within the length you want. Then make a line across the board using a square at the exact spot. Many woodworkers use a scribing tool instead of a pencil to get a finer marking. In this case, you would cut leaving the line behind, since it was within the length you wanted.
Also realize that when your finished cabinet meets other surfaces, such as the wall, it will almost never be an exact fit, due to slight irregularities in angle and levelness of the wall. This is where trim strips come in. While there is a technique for scribing an exact contour to fit a cabinet to a wall, that is a bit more challenging. Unless you are going to do that type of trimming, leaving a cabinet a hair shallow or short is much better than too deep or too high. Shims and trim work wonders.
Best Answer
Your circular saw will do the job, but you should make a jig to guide the saw instead of trying to follow a pencil line. You will need a couple of pieces of straight lumber a little longer than the cut you want to make. Many books and articles say to use scrap wood but I sometimes use good lumber destined for use later.
The technique is to cobble together an assembly with an inside corner that the saw's foot plate can be pressed against, with the piece to be cut positioned in the path of the blade. Sometimes you can clamp the assembly together but I find that the clamps get in the way so I usually use small nails.
The shape of the jig will depend on what material you have on hand to make it. Here is a suggestion:
Please forgive the crude cross section but it should convey the main idea.