First and foremost: what is your current cash situation? How long can you guys make it through the furlough? My inclination for right now would be to keep a whole bunch liquid so that you don't have the added burden of worrying about making ends meet. You have time to figure things out; being in or out of the market over the next month or two is not going to materially affect your future prospects.
Beyond that, I would pay off the student loan -- that's a pretty high rate of interest. I would also personally pay off the TSP loan; you need all of your retirement investments to be in the market, and so effectively loaning yourself money at 4% interest isn't great. Of course, both of those depend on there being non-furloughed people available to process the payoffs. I would not pay off the truck loan, as the interest rate is low.
If you pay off
@$12K of debt, that will leave you between $85-90K to play with. Figure out how much of that you need to set aside for your emergency fund to get you through the furlough, and put that in a savings account or money-market.
What you do with the rest depends on your priorities. Generally speaking, a 20% savings rate will put you in position to retire sometime in your 60s -- see
https://www.mrmoneymustache.com/2012/01/13/the-shockingly-simple-math-behind-early-retirement/. So if that is your goal, then go ahead and put the rest aside for a downpayment on a home.
OTOH, if you want to be able to retire earlier than that, then the money needs to go towards your retirement. A house is fundamentally a consumption item, like a truck or clothes: yes, you need somewhere to live, but you don't need a $700K house to meet that need, just as you don't need designer clothes to wear or a spanky new truck to transport you from one place to another; therefore, choosing to upgrade to those "nicer" options is a consumption choice, not an investment. And the key to FIRE is to keep your lifestyle costs as low in proportion to your income as you can while still living a satisfying lifestyle.
So I would recommend taking your furlough time to really work through all of that -- not just figuring out what investments and how to invest and all that, but focusing on what you want your life to be. How long do you want to work? How long do you think you will be physically able to work given the nature of your job? What do you need to save to be able to FIRE by that point? Are you and your family willing to live that kind of lifestyle? Or do you need to be planning on a longer working career in order to provide the kind of long-term lifestyle that will keep everyone happy. Etc. Once you have that larger vision, there are a bunch of people here who can help with the execution.