approval contingent on selling our current house.... YES. The timing would be a pita but yes VA and FHA will do that. Heck, if your DTI isnt an issue and they think you can handle both houses then approval contingent wont be an issue.
It is easy to get a mortgage approval subject to the sale of your home.
Getting an accepted contract may be a little more difficult unless your current home is under contract. It is easier to get the seller to accept a contract of yours is nearly ready to close. It is still subject to the sucessful closing of your sale. But then you are protected if the contract falls through for any reason. Make sure you let your agent and lender know you don't want two mortgages so s/he structures the purchase right.
As to debt: the lender looks a ratios and if you have rising debt (acclerating debt). I'm almost 95% certain they aren't looking at the type of debt but the LO's on this board will know more.
PS I am assuming you aren't running out and buying a bunch of toys like jet ski's, boats, fun & fast cars etc.