Hi Albert, you have an idea, but financially the ones with the highest interest should be pay first.
If one of the credit card is at 6% an another at 14%, pay the one at 14%. Remember that interest its something yu lose because of the use of the finance, it is not a product itself.
But, also, another idea could be to pay the smaller ones and then star paying the large ones.
Eitherway you need to star payign off your debt. Always pay more than the minimun payment. The more you pay , the better.
Holidays are just around the corner but you want to buy a home, so get your plan to do it.
Do not apply for more credit, magane your current credit cards.
Look for a Non profit or at your county for a First Time Home buyer program.