So you are after a time-controlled browser application, and nothing else? First question: do you have the BSP (board support package) for this device?
Yes: Modify the IESAMPLE source code, which is the browser that ships with CE, to have the display you want and remove things like the close button, and maybe even the caption bar. I'd probably even have it implement all of the required shell functions so it could run as the device shell completely. The IEShell sample would be a very good start. Then modify HKLM\Init in your project to have the reworked IESAMPLE launch at device boot and you're done.
No: It not going to be as easy, but it's still doable. Create an app using the IWebBrowser2 COM control that has the UI elements you want (like the above suggestions). Modify HKLM\Init to launch your app after explorer.exe (you probably will have to let explorer run to be a shell app) or if you do this in C++, implement the required shell functions. If you let Explorer run, then you need your app to find, disable and hide the Start bar when it initializes. How you get your app to persist will be hardware dependent - I know nothing about these devices.