Don't forget to take out 15% -20% from your budget to use for contingency costs during construction - all those unexpected things that are uncovered in older homes during a remodel.

We don't want a high end kitchen and will most likely go with IKEA for functionality. There is a bathroom in the basement already so it's just a remodel.

You could tell the architects that you have between 150-200K max. I think you should be ok except I don't know how much work your basement needs.
Is it a complete overhaul, are you adding a bathroom down there, etc.? Also, kitchen prices vary. You can spend 100,000 or more on the kitchen alone if you
want to go very high end. The kitchen will cost you at least 50,000 and the bathrooms might be $14,000 each. Master bath might cost more than that though.

We aren't adding on but enlarging kitchen/baths and opening a staircase. Based on your estimate, should we give $175k as our budget to allow for overages.

Your budget may work if you are not adding on.
I'm not sure you really need an architect or design-build for what you suggested unless you are planning to change the layout significantly.
Just give them your budget and see what they come up with. Plan for at least a 10-25% budget increase.

For a design build firm, maybe 10% of reno budget could be the architects fees, though in theory the "build" part is less. For an independent architect, $5,000-$10,000 for a project like that if no surprises? Depends on a lot of factors I don't know from what you wrote.

We are in process of purchasing a mid-century modern fixer and estimate a reno budget of $200k. We have a few meetings set-up with design build firms and full service architects to discuss the project. What budget number should we give them? We are looking at new windows, finishing the basement, and full kitchen and bathroom remodels (3 baths).