Which model did British, American and French use to build their state after their revolutions ?

1. Are they mostly inspired from Antiquity (Roman Republic), from ideas from XVII/XVIIIth philosophers (Hobbes, Locke, Rousseau, Montesquieu, ...), or from a mix of them (in which proportions) ?

2. Did they reject the idea of "democracy" and favored "republic" instead ? Why ?

Thank you