First: If you're doing this for a display at work, the place you work for should be buying the parts!!
You will probably want a setup something like this: 555 drives a binary ripple counter that's used to get the clock rate down to 1/3 to 1/5 Hz or so. (555's do not work well if you try to get a very low clock rate out of them directly.) This clock then drives a 4017 or 4022 Johnson counter with one-of-N outputs. If you don't want to use all of the outputs you can wire one of them to reset the counter. (Or you can build the three-state Johnson counter out of a few flip-flops.) So your counter would be doing something like 0, 1, 2, 0, 1, 2, ... and each of those outputs would control one lamp.
Re. AC, get it working driving LEDs first. Then change the LEDs to optocouplers, with the optos' outputs going either to relay coils or to triacs to switch power to the AC lamps.
Your absolute best bet for safety would be to use solid state relays like the one I've linked below. But three of those would blow your budget, even though they're heavily discounted (they're surplus), and you haven't even bought lamps yet.
Circuit design is not about finding diagrams that already exist. It's about finding building blocks that you can put together and use creatively.
I would be remiss if I didn't mention that you could also dispense with the individual chips and just use a microcontroller. Nobody builds stuff like this out of low-level logic circuits any more. The "obvious" choice, a regular Arduino, would set you back $30, or $25 for the Arduino Micro. But there are much cheaper options. For example the Adafruit Trinket would let you control those LEDs and it's just $8. Add power, optocouplers, and relays or SSRs. Done.
This gives you huge flexibility. Want to have a delay between one lamp going off and another coming on? Want to have different "on" times for the different lamps? Maybe even turn one lamp on slightly before you turn the previous one off? Not a problem. If you use triacs or SSRs you can even use PWM to get varying levels of brightness instead of just on or off. It's just a matter of changing a few lines of code. Of course you'll have to write that code, and program it into the controller. But that's what it's about these days.
p.s.: I disagree with Ken. Even with random logic, working out the logic is the easy part. If you think homebrewing something that runs on 120VAC and is going to be used in a commercial environment and making it SAFE is easy, think again. For that matter, there are almost certainly insurance provisions or fire code regulations at the workplace that prohibit the use of AC-powered devices that are not UL approved.