Looking for a chip

[lowimpedance]

Right now I am leaning toward using a CD4510 BCD counter as damo suggested.  I have a couple questions about the datasheet:

As I press the button multiple times, I am thinking the outputs 0₀s-0₄ will sequentially go from low to high.

OK I would check out some info on cmos logic ic's (ie search 4000 series) for operating conditions etc if i were you.
Also is your switch 'source' a clean debounced transition ??. (lookup switch debounce circuits).
Heres a chance to do some breadboarding and have some fun actually learning about digital logic, and then maybe move onto a 'simple' micro solution if you must.

[amyk]

If you're going to connect the inputs to the chip you're looking for to pushbuttons, how about a pushwheel switch? It counts automatically for you and displays the current value too.

http://www.ia.omron.com/product/42.html

[damo]

3.  Not sure I comprehend the operation...my thinking is as follows. 

I will connect P0-P3 to +voltage. 

I will connect +voltage through a push button to CP.

I will have UP/DW connected to +Voltage (for incrementing).

As I press the button multiple times, I am thinking the outputs 0₀s-0₄ will sequentially go from low to high.

Is this right, or am I smoking crack?

It's a BCD counter, to the outputs will go:
0000
0001
0010
0011
0100
etc...

Hence the need for a decoder circuit. A BCD to bar graph would require a considerable number of gates. I wonder what the minimum number of gates would be *fires up Multisim*