"Rule of Six" panel with some defects
There's a rule that you have to be able to cut power to a building with six breaker throws. Houses had been single main breaker, but breakers larger than 60A were prohibitively priced. So builders proposed this type of panel, with up to six of the cheaper <=60A breakers, which together are the "main breaker", rule of six. Your panel is a cheapie and only has four. (In some configurations it has five, as indicated by the label, that's why the "service disconnect" sticker is so tall). Fortunately your panel is also Murray, which is quality. I hope the builder really enjoyed the frappucino he financed by sticking you with a small panel.
The lower left of the "main disconnect" area has a 60A breaker. That powers the rest of the panel. That's right, the lower area, spaces 7-20, is already a subpanel. Too much load in that "subpanel area" will trip the 60A breaker.
Your main-breaker area is correctly configured. Your subpanel area has some defects.
- alien breakers that misfit the busses. Only the colored Murray breakers are correct; those black Cutler Hammer/Eaton BRs do not belong in this panel, are hazardous and should be replaced with Siemens/Murray, just like the panel instructions say. Total waste, the correct ones cost the same. Not even a frappucino here.
- double-stuff breakers in spaces 15 and 16 (upper right quadrant of subpanel area), that is not allowed per the panel diagram. Only full size breakers can go there, e.g. Move the big 2-pole up while changing it to Siemens.
Expect about a $35 bill on the correct breakers.
A subpanel is a grand idea
However you will want to power it out of the "main" area of the Rule of Six" (Four), as you have planned. I am not thrilled with the oven coming out of one panel and the range from the other, though. And this is a time to think about upgrades.
First, as you discussed, a service upgrade. You could plan for the subpanel to become the new main panel, perhaps indoors where it won't be insulted by painting contractors. It should be a 200A main breaker panel, and be positioned so running fat conduit to it from the meter will be easy.
Another thing to think about is generator. If you have aspirations for a generator, solar/battery system etc. it's time to look forward and see how to lay out subpanels for this, so you're not reduced to using one of those lousy "8-circuit changeover switch deals" that cost $350. It's really not far out of your way if you put your thinking cap on now.
I also trust you've heard the "Get a really big panel. No, Really big..." conversation, 42 space is literally not too much for a properly provisioned house. It's a few frappucino's today, but gives you liberty to do what you want. More kitchen circuits, done. Plug-in hybrid, easy. Hot tub, sure. Etc. There's no reason to be limited by your panel.
Lastly, tell you a secret. Your service drop is not 200A. Neither are your neighbors'. The power company didn't upgrade those. Huh!? The power company knows what drop you have, and what your electric bill is. (Also: smart meter). When they see you actually pulling more than the drop can handle, they'll come replace it.