Work's retirement pre-tax account is the 403b or the state level 401k or something different? Whatever the case since you have access to both a 403b and 401k, getting to a total of 19.5k from your contributions shouldn't be a problem even if limited to 6% on one vehicle.
Ignoring the 6% only contribution issue, of the 403b, 401k - I would go with index funds in whichever one has lower fees (accounting for any employer matching, of course) since these are not independent of each other when it comes to the IRS limit.
Similarly in the 457 options, check out the fees. If your employer is stable and the fees are competitive with the 403b, 401k - you might decide to fill up this bucket first (if filling both it doesn't matter) due to easier access.
Since you want to purchase a house, a Roth IRA will be a good (assuming your income allows you to make contributions) vehicle since you can withdraw the contributions. Even if you don't touch your Roth for a down payment, still great to have.
The investment order is a great place to start but the end result of finding your personal optimal order will vary greatly based on your situation (fees, income, etc.). But probably better to fill up tax-advantaged space as much as possible before funneling money toward a taxable account. Also remember there are various ways to touch your money prior to age 59.5 if you need to.
Lastly, read the fine print for your plans. Some 457 and 403b plans have additional catch-up provisions and not just for those 50+. This probably doesn't apply if early in your career but never a bad thing to know the ins and outs of your available plans.