Logo design needed and multiple explorations

We have a logo that we want to re-design, and create multiple options or variations from that initial re-design. We would like to start immediately to define the logo mark, and then create a set of collateral materials. Preference will be given to freelancers open to produce additional collateral pieces to enrich our startup branding efforts. Please tell us what you can provide, show us examples and give us costs. We are looking for a flat rate for this project, to project more work around this price model.