Can Asterisk do this for me?

I’m a small business owner looking for an inexpensive PBX system to route 2 POTS lines.

When customer calls line 1: play greeting, try ringing extension phone1 for 20 seconds, no answer go to voicemail.

When customer calls line 2: play greeting, try ringing extension phone2 for 30 seconds, no answer go to new greeting giving customers a choice to hang up or try ringing on-call cell phone via POTS first line.

If that makes any sense, could Asterisk do this easily?
If so, what hardware would I need?

I truly appreciate any replies!

yes! this is easily doable.

your hardware requirements are minimal.
Pretty much you need a PC, a TDM400P card with 2 FXO modules, and some phones.

You can got with standard phones if you want and order 2 additional FXS modules, but honestly. I"d recommend you’d go with a SIP phone, especially if you ever want to expand at all. Personally I LOVE the PolyCom 501 and 601 SIP phones… but there are some cheaper SIP phones out there if you are concerned about price.