First if possible, ask the initial *A carrier to interline the bags - most will, some don't

You need to have check bags 45 minutes before departure for most domestic flights. I would never arrive at the checkin area less than 90 minutes departure.

Getting you bags on international arrive may be 30 minutes but 60 minutes is common at many USA international gateways including ORD. Note ORD is no worst than others --- EWR, SFO, ....

On separate tickets I would never do less than 3 hours. Yes less can work many times But if you want 90+ success, be at least 3 hours with check bags. Checked bags or international arrival will be the longest item and GE will not make bags faster.