You've got a bit of a chicken-and-egg problem: you won't know the cost of any part of the project without developing at least some preliminary plans to show the scope. Ditto for interiors. However, if you wait until the plans are fully detailed to get the "punchline" you're likely to have wasted design money on a project that doesn't get built--at least not without some amount of redesign at additional cost.

I suggest you pre-select your team to include your architect, remodeling contractor, and interior designer. Share your overall budget with the team as a project objective and ask them to allocate the overall budget between design, construction and interiors. Then do a reality check: ask them to compare the budget with similar projects and see if what you have in mind is doable. If it is, then commit to do some preliminary design work. Get real-world cost information from your contractor and interior designer to inform the design. If it's not then you need to decide whether you are willing to pare back the scope or increase the budget.

I agree with what Charles said. The best projects are built with a collaborative team.

Thanks @Charles Ross Homes! I think that makes sense, but little scary to think you have to dive in blind. We've been told our project might not need an interior designer based on the scope, so as of now we're thinking of potentially using the architect as the interior design consultant as well. If we do that I would assume they'd do what you are suggesting by allocating design/construction and interior design budget, correct? I'm sure this is a common statement, but we don't have a huge budget, and may be asking for a lot, but being that this is the first time we've don't this we don't really know and we'll be leaning on the pros to guide us.

Some architects have interior designers on staff or at least some interior design competencies. If they don't, I wouldn't disqualify them; you should be able to find a local interior designer by asking around at furniture stores. I think you'll find that in a couple of hours they will be able to help you define your needs and set a budget for interior finishes.

Best wishes for a successful project.

Again, I agree with Charles. And a good interior designer should be able to review your preliminary plans in how they work with your furnishings to 'test' the spaces. Always good to do this before you get too far along in the process. Small tweaks like moving a door location or suggesting a floor outlet can make or break the success of the 'interior'.