Simple Home irrigation (pop-ups and drip) - valve box required?

I am having trouble Trying to understand your terminology. Pop up sprinklers require a specific flow to work properly, An example is that with your system you may only be able to run 3 at a time. If two many pop ups are installed on a branch they won’t cover the area they are supposed to. Most drip systems have very low flows but depending on the type of heads and number of devices you may need more than 1 branch , don’t put high flow devices like pop ups on the same branch with drip irrigation drip is low flow and may take hours to water the beds they cover where pop ups are high flow and usually are designed for 1 hour to properly saturate the ground.

Your valve box or manifold concerns, there are many different ways to set a system up, some have a manifold with all the valves at the source, some run a single supply line and have valves branching off where needed so wires are run in ground (usually low voltage wire and valves 6” or more below the surface).

Both styles have merit but depend on the layout to which makes cost sense.

The last topic is are you on city water or well water, both have pluses and minuses but city water usually requires a back flow prevention device or valve on sprinkler systems.

The main cause I have seen in poor designs is two many sprinklers per branch for the available flow. Keep learning and I am sure you can build a system that will meet your watering needs, I used to do valves great way to start, then move up to full controllers where my last home had 24 branches to do everything even 1 outside that filled a water feature , birdbath , and the dog bowl outside yes you can go crazy but it was also fun.

Yes, you need a valve box for your own convenience.It will have low voltage wires running to the valves. You will also want access to the valves to use the manual feature - activating pop-ups on that line to check operation. Boxes I see can hold about 3 valves. Valves can be buried but that is a bad idea. Not to disagree with @ ed beal , I have put up to 5 popups on one 1/2" line , and mixed soaker hoses with pop-ups. If you are on city water you will be required to have a costly antisiphon valve. As said , systems can be very versatile.