I’m wondering if I can connect about 15 or 20 low voltage, 1 inch by 1 inch solar panels directly to a home 120V power circuit without any inverters or extra equipment?
NO! You need special equipment to make any hook up to the electrical system. Solar panels are direct current or DC and your electrical service is alternating current or AC. You would need inverters and phase matching equipment to make those kinds of connections.
For a Photovoltaics system to work properly you will need batteries for storage, wiring to handle the system amperage , inverters, phase converters, and fairly large arrays of solar panels to make the system worth while.