With how different site are these days I find it best to decide the budget individually.

Page on your site including all the design information. This will inform other designers how to implement future changes while staying cohesive and worry this is not published so the clients won't see it.

simple sites with one or two pages: between 1-2 weeks Advanced site e.g. e-commerce or a portfolio might even take 2 months based on the complexity.

There is no need however if you have a vision for it you can share some inspirations.