First of all, congratulations on admitting your problem and on your determination to be debt-free. Recognizing your mistakes is a huge first step, and getting rid of your debt is a very worthwhile goal.
When considering debt consolidation, there are really only two reasons to do so:
Reason #1: To lower your monthly payment. If you are having trouble coming up with enough money to meet your monthly obligations, debt consolidation can lower your monthly payment by extending the time frame of the debt. The problem with this one is that it doesn't help you get out of debt faster. It actually makes it longer before you are out of debt and will increase the total amount of interest that you will pay to the banks before you are done. So I would not recommend debt consolidation for this reason unless you are truly struggling with your cashflow because your minimum monthly payments are too high. In your situation, it does not sound like you need to consolidate for this reason.
Reason #2: To lower your interest rate. If your debt is at a very high rate, debt consolidation can lower your interest rate, which can reduce the time it will take to eliminate your debt.
The consolidation loan you are considering is at a high interest rate on its own: 13.89%. Now, it is true that some of your debt is higher than that, but it looks like the majority of your debt is less than that rate. It doesn't sound to me that you will save a significant amount of money by consolidating in this loan. If you can obtain a better consolidation loan in the future, it might be worth considering.
From your question, it looks like your reasoning for the consolidation loan is to close the credit card accounts as quickly as possible. I agree that you need to quit using the cards, but this can also be accomplished by destroying the cards. The consolidation loan is not needed for this.
You also mentioned that you are considering adding $3,000 to your debt. I have to say that it doesn't make sense at all to me to add to your debt (especially at 13.89%) when your goal is to eliminate your debt. To answer your question explicitly, yes, the "cash buffer" from the loan is a very bad idea.
Here is what I recommend: (This is based on this answer, but customized for you.)
Cut up/destroy your credit cards. Today. You've already recognized that they are a problem for you. Cash, checks, and debit cards are what you need to use from now on.
Start working from a monthly budget, assigning a job for every dollar that you have. This will allow you to decide what to spend your money on, rather than arriving at the end of the month with no idea where your money was lost. Budgeting software can make this task easier. (See this question for more information.
Your first goal should be to put a small amount of money in a savings account, perhaps $1000 - $1500 total. This is the start of your emergency fund. This money will ensure that if something unexpected and urgent comes up, you won't be so cash poor that you need to borrow money again. Note: this money should only be touched in an actual emergency, and if spent, should be replenished as soon as possible. At the rate you are talking about, it should take you less than a month to do this.
After you've got your small emergency fund in place, attack the debt as quickly and aggressively as possible. The order that you pay off your debts is not significant. (The optimal method is up for debate.) At the rate you suggested ($2,000 - 2,500 per month), you can be completely debt free in maybe 18 months.
As you pay off those credit cards, completely close the accounts. Ignore the conventional wisdom that tells you to leave the unused credit card accounts open to try to preserve a few points on your credit score. Just close them.
After you are completely debt free, take the money that you were throwing at your debt, and use it to build up your emergency fund until it is 3-6 months' worth of your expenses. That way, you'll be able to handle a small crisis without borrowing anything.
If you need more help/motivation on becoming debt free and budgeting, I recommend the book The Total Money Makeover by Dave Ramsey.