I bought a HF router (1.5hp 1/4 Collet) a while back on sale in case I ever needed one.  Well, I want to "trace" 1/2" MDF and 3/4 Plywood for an Arcade project now.  If I am doing a straight through cut (is that a thing?) I would think I should use the smallest bit possible right?  If rough cutting with skillsaw first it doesn't matter because I'm just trimming excess?  

You will get horrible tear out doing that with a router.  Best way to do this is on a router table with feather boards extremely tight to the wood and running the plywood backwards across the bit.  If your feather boards are not tight enough, the bit will pull the plywood out of your hands and shoot it across the room.  

YMMV but this is my experience with plywood and router bits

If it were me, I'd clamp the template to the plywood and trace it out with a pencil.  Then unclamp it and use a jigsaw or bandsaw to cut outside your line by about 1/4".  Far enough away that the roughness and tearout from the jigsaw blade is not inside your line.  Then clamp your template back onto the plywood and use the guide router bit to trace around it and clean up that 1/4" you left.

You absolutely *can* cut the entire thing out with a router if you wanted to.  However, the router will be a lot slower and make 870000% more sawdust.  Also, when taking bigass cuts with the router, like the full width of the blade and the full depth of the plywood, that is asking a lot of it.  You're more likely to get kickback, ugly cuts, and burning the bit up.  If you do want to use a router to cut something out, its best to make multiple passes, going deeper each pass.  That is not something thats easily done with a template bit with a bearing on it like you're got.  It can be done if your template is thicker than your plywood by a large margin.

Yep, jigsaw (or bandsaw if possible for a given part, probably not in your case) then clean it up with the flush trim bits.

Guess if you're feeling really ballsy you could try it with a CNC endmill... lol. Regardless tearout would be very bad.

I've used flush trim bits plenty of times on plywood to build speaker boxes. Never had a tear out issue.

A 1/2 inch diameter is a good size. It's stout enough that you won't risk breaking it as easily or get a bunch of vibration on the bit.
 
The suggestion to remove most of the material with a saw them trace with a flush trim is what I would do. You will be limited with your router if it only has a 1/4 collet though to mostly just smaller bits.

1/4" two flute spiral upcut carbide bit is what you seek.

I appreciate everyone's advise, looks like it will more difficult that I expected.  I took the curves out of the design and will only have rounded corners.  Will rough cut with skill saw and guide bar.

Some things you can do to reduce tear out.

1. Place masking/painters tape over the area to be cut. This helps hold the fibers down to minimize tearout.

2. Score the cut line. If you are doing a straight section, score the cut line with a sharp knife and straight edge. You need to be precise, but scoring is magical when done well.

3. Use a spiral compression bit (Whiteside makes some good ones). When spiral bits cut they tend to push fibers out on the top or bottom depending on whether they are upcutting or downcutting. Compression bits push in toward the middle from both sides, leaving cleaner edges. They are also pretty expensive and cost more than your HF router.

4. Back the workpiece with a sacrificial sandwich.

Finally, make some practice cuts. Look at the end product of the cut and decide whether it is good enough for your purpose.

You want a down cut or up cut spiral bit, they shear better and leave less tear out.
If you can't find one with a pilot bearing, you can use a collar and adjust the size of your template.

I'd also use 1/2" collet bits, less chatter.  Make sure to go the right direction, no climb cuts.  Use a new bit.

Use blue painters tape along the cut line.

Use good quality plywood like Baltic birch.  Or multi ply poplar.

If you're applying plastic laminate and T molding, tearout isn't a huge concern.

In general, with a standard non spiral bit, a larger diameter bit will have less tearout because the angle of cut is more perpendicular.  
I have a 1 1/2" template bit for exactly this purpose.

I didn't have a lot of choices on the plywood because I wanted pre-sanded.  Got 3/4" Birch and 1/2" "Blondewood" already.  One project will get expoxy so edges will be finished with Bondo or Glaze, the 1/2" Body glaze or putty (will be painted)

I assumed the bits were made cut from bottom to top, is that correct?

I will have to find something to use as a guide for the rounded corners.

Here's a good video on router bits.

https://youtube.com/shorts/5L8BVQffdHQ?feature=share

How close to Charlotte are you OP?  Be happy for you to come over and use my wood shop.

5 hour drive (Greenville).   I think it's going to be OK, just going to practice on a smaller piece first.

So it was taking so long moving around guide bar for skill saw I did up just routing it out.  I don't have a proper workbench so I have move it around a few times over my cerakote oven.  Much, much easier than I expected.