What's more important: 1) square footage; 2) maximum budget?

Whatever is most important is what you work with the builders to achieve.

Good luck on your project.

Is 350K the max you are approved for or willing to spend? If so, I would tell them a lower number since you will most likely go over. We told our builder our budget was 300K, we were approved for 375K, comfortable going up to $330L (did not tell builder this, of course). He came in at 308K, loan amount will likely be 320K with closing costs and other upgrades.

I asked several builders for an average price per square foot on their projects when I was interviewing them without giving them an indication of what we were willing to spend. I don't think you need to share your budget up front. You may also be limited by the area you want to build in - for example, we are building in an older neighborhood in Houston where the housing stock is being torn down and rebuilt, so while the market is on the way up, I didn't want to overshoot the price per sq. ft. to a point that we couldn't sell without taking a $100k hit, regardless of what we could technically qualify to borrow.

Maybe not tell them preliminarily, but you need to get them in a range that is fairly close or you will waste each others time. If your budget is $300,000 and they think your budget is $400,000 or you are discussing a house that will cost $400,000 to build no matter your budget, you just wanted a lot of time.

You would always tell the designer your budget but you would never tell a contractor your budget.

This is just the first of the many conflicts of interest you will discover in a Design-Build approach.

This is the only way we feel we can afford a custom home (architects charge 5K and more in my area, whereas the home design is included in the contractors plan).

could i ask something like: would you be willing to build a home similar to X (point out a home they've already built) for 80 per sf? or is that too vague?

Get a rough idea of the plan you have in mind, #bedrooms and square footage, # garage stalls etc. Rough sketch it out, list some basic finishes like flooring and countertop types and let them shoot you a price/sq. ft based on your general idea. Weed out the outliers and then work with whom can come in close to your budget. Its all negotiable. You will also get a better price/sq. foot buying a plan the builder is experienced building so if you have a chance to peruse their plans they can tell you what it would cost exactly. They are familiar so they don't budget in the "unknown" like on a full custom job. Good luck.

Design-Build is not necessarily cheaper; you could easily save $5,000 by bidding your project competitively and perhaps more during the construction phase.

I don't care how you do it but you should at least be aware of the common pit falls and false economies of Design-Build.

If they give you a cost per square foot, you should be aware that that number may be based on assumptions that do not apply to your project. For example, it might what he can do if you choose a plan of his that he's built before, on a prepared lot.

I would not just ask what they typically charge per square foot, but what they would charge for a project like yours (although there's a limit to how accurate they can be in estimating the cost of a not-yet-designed house).

If they are designing your house they need to know your budget. And if you want it built it for as cheap as possible you shouldn't have your contractor design and build your home. You should finalize your plans and have it competitively bid by 5 GC's.