Disclaimer: no pocketCHIP yet, but I spent plenty of years using GUI browsers on my Zaurus PDAs, as well as remotely logging in to my Raspberry Pi.
All (or almost all) of them (browsers and desktops) will allow you to configure them to fit your desired screen resolution. But it often does require some research. Both Zaurii had screen smaller than the PocketCHIP has, and while I started out using LXDE remotely as a desktop environment, I decided that was heavier than I needed and ended up settling on Openbox with lxpanel for a system tray.
I did not get adept at using LXDE, so all I know well is Openbox, and I know in that I have the choice of hitting an icon at the top left of my screen to bring up a menu that gives me various options, including increase or decrease the size of the display for the application that is running. But they all have configuration files that allow you to set the default screensize. And this is generally possible to do from a settings GUI, it does not require changing configuration files from the command line, although that is generally also possible.
Besides looking for how-tos on the specific desktops or window managers you want to use, poke around in your home .config directory to see what configuration files are already there for installed applications.
I like using lxpanel to switch between applications on my Raspberry Pi, but am thinking I don't want to lose screen height on the PocketCHIP to a bottom tray. However, lxpanel has the option of putting the the tray on either side, and I am thinking of putting a very narrow tray on the left side of the PocketCHIP's screen, with just icons to click on to change between running apps.
And one of those icons will bring up a popup menu of applications to choose from, that are already installed. i never could figure out how to get apps on a desktop, so if I don't want to start an app from command line, then I go to the bottom tray and the leftmost icon, if I click on it, lists all applications that have a desktop entry for themselves.
But it is so many years since I installed this, that i do not recall offhand where the launchbar came from, I think it was part of lxpanel and might be called pcmanfm, but am not sure.
Anyhow, whatever you want to run, if the menu bars are too big or unnecessary, or you need scroll bars, that all is possible to change by modifying the settings to meet your needs. This has been summarized in other threads with statements something like "this is Linux, you can configure anything".
One of the things I like about Openbox is the ability to define hotkey combinations, and to do keyboard mouse emulation. My experience with both Zaurii with the same kind of resistive touchscreens is that even with using a stylus that is the right kind of plastic, at some point, those places one taps a whole lot, the screen will likely wear down at those points, so I am wary of doing too much with a stylus.
I like the fact that PocketCHIP uses resistive touchscreen, though, as I really do not want to learn "gestures". I am used to working with a resistive touchscreen.
Never got comfortable with using mice, so I love the mouse emulation possible with xwit and xdotool that I define in my openboxrc file.
Anyhow, I am not the least bit worried about being able to get browsers and other apps working well with the small screen, despite other people's comments about how awful it would be. I mean, I have spent a good part of the last decade or so with my only screens being smaller than that of of the PocketCHIP, check out the Zaurus sl5500 and sl600 if you want to see what I mean, both screen are smaller.
If I needed to visit a webpage that required a larger screen ( and it is the webpage, not the browser, that would really be the issue), then I learned to VNC into a friend's box with Firefox, and had my Xvnc seet with the screensize I found would work best with my tiny screens. I did need to scroll around to the left or right, but there were scrollbars both in my vnc client as well as the remote Firefox.
For your searches, I would just look at Settings for the applications themselves. Pick something you want to use, and just modify it. Also, if you are turning up examples about how to increase screen size, and they talk about changing the settings, just pick lower numbers that fit the screensize of the PocketCHIP.
Try hitting the F10 (the function key, however you bring it up with PocketCHIP's keyboard), that usually brings up menus on stuff already installed, and check out the contents of the various dropdown menus that appear. Often there is a View option with the ability to zoom in or out or set a custom font size.