Your counter circuit needs a pull-down resistor on the reset line. Also, the 4026 is not really built to drive displays directly. The datasheet has three display application circuits, and all of them have external drivers of some kind. You can drive one display directly, but it will not be very bright and should have 7 current limiting resistor, one per segment. That's 21 additional resistors on your schematic.
Another approach to the counter is the CD4553 / MC14553. This is a 3-digit counter with a display multiplexer built in. It needs one decoder/driver and one set of 7 resistors, so the net circuit body count is lower.
And finally, the Intersil ICM7217 (now made by Maxim), a 4-digit counter complete with decoding and display driving built in. It is the all-in-one solution, a bit of overkill with presets and comparators that you can ignore.
ak