I really wonder who told you that PIC is simpler than Arduino

PIC would be my #1 choice but i happen to know about PICs already. Regarding the TTL circuitry, if you plan to make it for educational purposes then this would be the best solution, but if you plan to make something that will work without anyone care how it works, then go with a microconotroller.
As for the PIC, i suggest you start with the 16F88. It is not as cheap as the one that cheerio suggests, but I have an
on-line guide to help you start based on this chip. Actually, this chip is rather an expensive one due to its capabilities (a load of modules and protocols).
- With mcrocontrollers you can leave your imagination free regarding the time selection. An LCD for example with a rotary switch can be used to set time.
- Or you can go with a simple potentiometer
- Or you may wanna use 4 buttons which will set a 7-segment counter (2 buttons for hour up-down, 2 buttons for minutes up-down)