Design Timer circuit
As is evidenced in the comments, you should consider using an off-the-shelf solution such as a micro-PLC (programmable logic controller).



Figure 3. A micro PLC with keypad and LCD.

The small DIN-rail mounted types typically feature eight inputs and four outputs on the base module with expansion modules available to plug in or network connection. The one in the photo is from Crouzet but most of the big manufacturers - Allen-Bradley, Siemens, Mitsubishi, etc., have a version. You would require the AC-powered version with relay or triac output to power a contactor for your application.

For a very basic sequence as you describe they can be programmed from the front panel. For more complex jobs you will need the programming software.

Prices in Europe are typically somewhere around €100.