What to do with 25k?

Houses are a flat or losing investment these days, wouldn't put the money there.  Unless you live in one of a couple of cities where real estate is going up, I wouldn't trust the appraisal.  In fact, I've not seen one house in our area sell for the appraised value, it's always at least 5% below and sometimes the difference is much, much more significant.  If the bank appraised the house for HELOC qualification purposes, check with them.  They often won't loan up to 100% debt to equity on a house these days, so your HELOC may be limited.

In my specific situation, I'd do the following:

Student loan rates are fixed.  HELOC rates are not (generally).  I'd leave the student loans where they are.

Food and emergency preparedness storage can be built over time.  You'd be amazed at how quickly the stuff builds up.  Do that our of your regular paychecks if you can.

Credit card interest rates can change in a flash. I'd pay off the credit card since that would open up discretionary/emergency buying power if it was ever needed (i.e., food storage, fuel, more gold).  That takes away $10K of your $25K.

Invest the remaining $15K in 2-3 recession resistant vehicles, such as gold, silver, oil, commodities.  Hedge a little with a solid dividend paying defensive stock.

That's just me.  I had a very similar amount of money come my way a couple of years ago, and the shiny stuff I bought with it is now at the bottom of a lake due to an unfortunate boating accident.   Seems like every time I build a new shiny stack, I have a boating accident in exactly the same spot.

i personally would consider selling the house, if possible while you still can and either rent or downsize, and pay off the student loans, highest rate first, then work on credit card debt as each time you roll that debt you will pay 3 percent or more up front as the zero percents don't last forever and will soon be closer to 10 percent. i don't know what your line of work is or your income or your prospects for remaining employed. I just know that now is not the time to be massively in debt.

Enliven,
You may want to consider doing several things with your 25K windfall.

1) Accelerate payments on your student loans to shorten the term significantly. (see examples below)
2) Stash some greenbacks for emergencies. (a few thousand could protect you in the event of a bank holiday or other financial crisis)
3) Put some part  of your 25K "windfall" into bullion coins. 
4) Get rid of the 10K credit card debt even if it is 0%, that low rate won't last.

As far as the preparedness items, a good water filter ($250 for a Big Berkey) and a well stocked pantry won't set you back that much. You can add to your preparedness inventory on a regular basis. (out of income)

RE: Student Loans. I never had a student loan but if they are anything like a mortgage payment, you can make additional (monthly) payments and drastically reduce the length of the loan by chopping away at the principal. You can find a user friendly amortization calculator on many internet sites, the one I just used is on bankrate.com.

Example: If your monthly payment on the 7.45% 40K student loan is approximately $270 and the loan has 30 yrs on it, you can make an additional $270 every month (doing this requires discipline and sacrifice) and reduce the 30 year term to something like 8 years. Not bad! Another way to look at prepaying is that you are earning a 7.45% return on any extra payments you put towards principal.
A 7.45% return is pretty good nowadays.

The key to this form of debt reduction is to develop/choose a plan and stick with it.
The loan amount due will melt away in less time than you think.
You can plug in any payment amount and the amortization schedule calculator will let you know how much that added payment will shorten the loan term.

I wouldn't take out credit card loans for 0% teaser rates unless I had an extremely well defined, short term and productive (profitable) use of the money with a certainty of being able to pay it back before the teaser rate ended.
I hope some of this helps. Good luck!

$25k. Whatever you do, do -not- blow that cash paying down debt. You want to keep your liquidity; sometimes being able to show "X" amount of money/ months of debt payments in the bank can get you favorable terms for 'whatever'...ie a refinance, a loan, etc.

Get a US passport.

$12.5k stays in cash reserves with a reasonable amount hidden ($2.5k) in a safe place at home i.e. 'never touch' money kept in 100's,20's,10's and 5'. 100 bucks worth of 1's.  You will make the min payments on your 0% cc's or in a crisis, pay down the entire amount. Keep enough around to pay, in cash, for a 1-way plane ticket to the country of your choice.

$12.5k -> 7.5k metal. Shoot for 80oz silver maples and 20oz worth of junk dimes and whatever amount of 1/10 gold eagles you can swing with the difference.

-------> $5k prepping items: Basic array of camping gear with the intention of car camping: ie. quality sleeping bag (REI level). Self protection. Combination of bulk storage foods, some freeze dried camping stuff, some MRE's, some 'extra' canned goods you normally eat. Don't go too heavy on something like thrive. Try to assemble a minium of 3 months of food. Try to go for 6-9 months. I would not recommend a Big Berkey, I would recommend a katadyn pocket filter. Reason being: Big Berkey is not mobile. If you are forced to abandon your home and hit the road, you are SOL.

2" hitch for the Escape; Curtis hitch via Amazon should be around $130 bucks and self-installable. $200 bucks worth of new Nato gas cans (4 x 5.28g/can) from Deustch Optik. Harbor Freight 2" aluminum cargo carrier to carry this fuel. Get hitch pin while you are there. Get an appropriate funnel and a shake-fuel transfer hose.

http://www.amazon.com/Super-Siphon-Hose-TWO-16-95/dp/B000ZORJ1E

You have now effectively doubled the range of your vehicle and can carry bulk food items in the tray.

You want to stay mobile and able to reasonably relocate out of the immediate area, out of state, or out of the country if need be.  Don't get too wrapped up on the cc debt; keep paying that student loan debt down though...do not pay that off early b/k you can defer it if you have to. I learned a memorable quote late last year: Never be married to the idea of how you think things are going to go down.